Draft is a Limited format wherein players divide a limited and usually random pool of cards among themselves by a predetermined method, then construct decks from the cards they drafted plus any number of basic lands and play using those decks.
The most common type of draft is the Booster Draft, in which each player starts with 3 booster packs. Simultaneously, each player opens their first pack, takes a card, and passes the remainder of the pack to the next player, before taking a card from the pack received from the previous player. This continues until the first set of packs is depleted, at which point the second pack is opened and the process continues with the passing direction reversed. And again for the third pack, with the direction reversing a second time. Players are then provided any number of basic lands, and construct their decks from their drafted cards plus those lands.
Other draft formats include Rochester Draft and Cube Draft.