Using the Card Drafting mechanic each player starts with x number of cards, and chooses a smaller number of cards for their 'hand' before passing the remaining cards to the next player. Then these cards are reviewed and that smaller number is selected again for the 'hand' from the remaining cards. This passing and selecting continues until each player has a hand with x cards in it.
The only game currently in the library's collection that has even a small amount of Card Drafting is Ticket to Ride. In this game, mainly built on the Set Collecting mechanic, some of the cards available are in an open pool that all players can see and choose from. On a players turn they can choose one of the following: select two cards (either from the open pool mentioned above or from the face down draw pile), play a set of cards to claim a route on the board, or draw new tickets. When they select two cards and use the open pool they are 'drafting' them away from the other players.