Stock Pile:

A pile of face-down cards that players may draw from; located to the left of the Discard Pile. 

Discard Pile:

A pile of face-up cards that players may discard to and draw from; located to the right of the Stock Pile. 

Hand:

A personal collection of 7 or 10 cards (depending on your settings)

Meld:

A Set or Run of cards in a player's hand; also known as a "lay". 

Set:

One type of meld. A collection of 3 or 4 cards of the same rank; also known as a "group". 

Run: 

The other type of meld. A collection of 3 or more cards of the same suit in sequential rank; also known as a "sequence". 

Lay Off: 

Adding one or more cards to an existing meld on the table.

Go Out: 

Playing or discarding the last card in one’s hand. This ends the round and scores points for the player who went out.

Rummy, or "Going Rummy"

Playing one’s entire hand in a single turn. This is worth 25 bonus points, which is applied during the scoring sequence.