Some Basic Dancing Terms

The Caller - The person who gives the instructions (ie calling) the dance.
The Set - The collective term for the dancers.
The Formation - The position from which the dance is started. There are many different formations, the most common being:
Circle - A circle around the room with the lady on the right of her partner.
Longways - Everyone faces their partner to make two long lines with the men on the caller's right and the lady on the caller's left. The set may have any number of couples, but some dances may have a fixed number such as three, four or five couples.
Sicilian Circle - Couple facing couple and each group of four making a larger circle around the room.
Square - A four couple set with each couple on the side of a square with the lady on the right of her partner.
Beckett Formation - A longways set but with the lady on the right of her partner facing another couple across the set.
Hands Four - This is a term used by callers when a set is being made up, to define first and second couples. This divides a longways set into subsets of two couples who temporarily hold hands to make rings of four. The couples nearest the band and the caller become the first couples, with the others becoming the second couples. Sometimes hands 6 or 8 may be used for special dances - see also Triple minor below.

Progression - Many longways sets will have started off with "Hands Four". The progression will be for each first couple to move down the set to a new second couple and each second couple to move up the set to a new first couple. When a couple reach either end of the set they normally stand out for one turn of the dance. If it is an "improper" dance, couples should change sides with their partner whilst standing out. For Beckett dances, couples progress down one side of the set, across the end and up the other side of the set.
Proper and Improper - A proper dance is one as described in "Longways" above where all the men are on one side of the set and all the ladies on the other. An improper dance is where the first couples have crossed over with their partners in a longways set. An indecent dance has the second couple crossed over instead of the first couple (mainly in contra dances).
Triple minor - Some longways sets work with three couples dancing together rather than two couples. In this case the caller will have started with "Hands Six" rather than "Hands Four".

Allemande Left - Give left hand palm to palm to your partner or to whoever instructed and walk a complete turn anticlockwise back to place.

Allemande Right - Give right hand palm to palm to your partner or to whoever instructed and walk a complete turn clockwise back to place.

For safety, during an allemande it is considered good practice to keep the thumb flat against the hand rather than hook the thumbs around each other. There have been cases of dislocated thumbs during energetic allemandes when one dancer doesn't release quickly enough.
Back to Back (also called a Do-Si-Do ) -Take two steps forward (to just pass partner's right shoulder), one side step to the right and two in reverse passing left shoulder to finish back in place.
Box the Gnat - Man's right hand to lady's right hand, both walk forward passing right shoulders. Lady twirls away from the man as she goes under the arch. Each will be standing in the other's original position and facing each other.
California Twirl - Man's right hand to lady's left hand, the lady walks under the arch as they trade places and face the opposite direction from the start of the figure.
Cast - Turn away from partner and move to the position instructed.
Changes of 2, 3 or 4 - (of a hey, or of a circular hey, or of a square through) is similar to right and left through but without the courtesy turns. It may also be done without hands and just passing shoulders.

Double Figure of 8 - See figure of 8, but done by two couples at the same time around each other.
Circle Left (or right) - 3 or more dancers join hands and circle to their left (or right).
Figure of 8 - One couple stands still whilst the other couple, with the lady passing in front of the man, go between them, around the person on the opposite side of the set, between them again and around the other stationary person to finish back in place.    
Man's track           Lady's track
Gender-free Calling - Calling a dance without reference to gender i.e. the use of men/women, or ladies/gents. Instead, Larks and Robins are used, which translates back to men and women. Also see Positional Calling. In contradancing it is becoming more common for people to dance either role i.e. men dancing what was the ladies role and vice-versa, and to swap roles during the dance. This gives the opportunity to experience the whole dance, rather than just one role.
Gypsy Right or Left - Facing partner (or whoever instructed to gypsy with) and circle around each other to the left or right (as instructed) without hands until back to where started, all the time gazing into that person's eyes (it's a flirting move). Also see Right Shoulder Round.
Gypsy Meltdown - Gypsy right one full turn then naturally go into a swing. A contradance move. The call is now 'Right shoulder round then melt into a swing'. Quite a mouthfull!
Grand Chain - Walk around a circle or along a line giving alternate hands for the number of times (hands) instructed or until back to place. Normally started with right hand.
Honour - Face partner (or whoever instructed) and step to right, stay there and acknowledge that person. Often followed by step left and acknowledge.
Ladies Chain - With two couples facing and a lady on the man's right. The ladies cross the set, giving right hands to each other to pull by and give left hand to the opposite man's left. The man puts his right arm around the lady's waist to turn her around (courtesy turn) so that the two couples are again facing and the lady is on the right. Often (but not always) the movement is repeated from the opposite side so that the ladies get back to place. In positional calling this will be a Right-hand chain.

All Four Ladies Chain - Similar to ladies chain but often done from a square formation. The four ladies give right hands to make a star and go half way around to the opposite man who courtesy turns her out of the chain.
Left Hand Star - Usually danced by two couples giving left hand to the diagonally opposite person to form a cross and walking in an anti-clockwise direction to finish back in place.
Lead - Take nearest hand with partner and move as instructed.
Left Hand Turn - The man gives his left hand palm up and the lady puts her left hand into his, palm down. Walk a complete anticlockwise turn back to place. Gently grip (without thumbs) so that each dancer can pull away easily - it has been known for a dancer to grip tightly and not let go!
Men's Chain - With two couples facing and a lady on the man's right. The men give left hands to each other to pull by and give right hand to the opposite ladies left. The lady puts her left arm around the man's waist to turn him around (courtesy turn) so that the two couples are again facing and the lady is on the man's right. This move is rarely done but more (contra) dances are being written incorporating it. In positional calling this will be a Left-hand chain.
Mezcolanza - sets of normal-facing lines of four i.e.  two couples facing two couples, with the sets stacked up lengthwise down the hall away from the band. The lines of four with their backs to the band progress down the hall away from the band, while the lines of four facing the band progress up the hall. Within each set of four, couples usually change ends with each turn through the dance, as part of the dance.
Positional Calling - Calling a dance without reference to men/women or larks/robins. Instead, the positon of the dancer is used, and which hand happens to be free i.e. right-hand chain where the person on the right of the couple uses their right hand to pull by the person on the opposite side of the set.
Pousette
Full pousette: Give two hands to partner and with one pushing (as instructed) forward four steps moving slightly to the side and reverse back into other couples place. Continue with other partner pushing to return to place.
Half pousette: Give two hands to partner and with one pushing (as instructed) forward four steps moving slightly to the side and reverse back into other couples place.
Draw pousette: Give two hands to partner and with one pulling (as instructed) move in a semi-circle around the other couple. Couples will have swapped places and changed sides in the set.
Promenade - With lady on man's right hold right hands and left hands and move forward, usually anticlockwise.
Right and Left Through - Give right hand to opposite person and pull by, face the next person in the same group of four and give left hand and courtesy turn to end facing the same opposite person again, but from the opposite side of the set.
NOTE that right and left through and back means continue the same move until you are back to place.
Reel or Hey - Usually done with 3 or 4 people who weave in and out along a straight line until they all get back to Place. Sometimes done as couples or in two lines at same time as partner.
Right Hand Turn - As for left hand turn but with right hands and walk clockwise.
Right Hand Star - Usually danced by two couples giving right hand to the diagonally opposite person to form a cross and walking in a clockwise direction to finish back in place.
Right Shoulder Round - Slowly replacing Gypsy Right, especially in contra dancing. Why the change? Something to do with political correctness...
Set (or Balance) - Take a step to the right and bring left foot to it introducing a slight bounce by putting more weight on the leading foot and move left foot back followed by the right with a similar bounce. An alternative, usually used in contra dancing, is to hold both hands with your partner and step forward and back; the move allows both partners to 'give weight' and gently pull each other into the next move, often a swing.
Siding (Cecil Sharp) - Facing partner throughout. Walk 4 steps forward passing partner by left shoulder and 4 steps back passing right shoulder. Also known as "banana siding" because of the curved shape of the walk.
Siding (Pat Shaw) - Walk 4 small steps forward to be right shoulder to right shoulder with partner, reverse to place. It may be repeated with left shoulders.
Star Through - Man's right palm to lady's left palm, both walk forward passing right shoulders. Lady twirls away from the man as she goes under the arch. Man has turned to the right, lady has turned to the left.
Swat the Flea - Man's left hand to lady's left hand, both walk forward passing left shoulders. Lady twirls away from the man as she goes under the arch. Man has turned to the left, lady has turned to the right.
Swing - Using the ballroom hold, men stand slightly to the left of partner and walk they around each other (this is the American walk swing).
OR
With the same hold, each put the right foot into the centre and use the left foot to push off as if riding a child's scooter in a circle (this is the buzz-step swing).
Turn Single - Turn on the spot (normally to the right) in four small steps.
Two Hand Turn - Give two hands to (either your partner or whoever instructed) and walk a complete turn clockwise back to place. It is etiquette for the man to hold his hands palm up and for the lady to put her hands onto his palm down.