An out is a card that has not yet been observed to be dealt out of the deck, which if it is dealt into your hand, or into the community cards you can play, will make your hand (give you the powerful hand you were drawing for).

Outs are generally used in calculating pot odds, since the number of outs you have divided by the number of unseen cards in the deck is the probability you will get the out and make your hand. You then use this probability to determine if the pot is large enough to justify a call.

A few examples are probably the best way to illustrate this concept:

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