Drafts are about being able to size up the relative strength of cards and dynamical evolve your Army strategy.
Draft Tournaments start with a drafting phase. Each player is shown a pack of cards and picks a card from this pack to be in their draft collection. After they pick a card that pack is rotated to the next player and they get a new pack to choose from. The packs rotate around until all 15 cards are picked. Then a new pack is given to each player and the process repeats. You open 3 packs this way. Once you have picked your 45 cards you build your Army. Your Army must be at least 25 cards and can have any of the cards you drafted. Once each player has submitted their army the play proceeds like a Constructed Deck tournament.
Again these can be either single or double elimination.
Keep Cards Draft
The Keep Cards Draft costs 500 gold or 50 Power to enter.
Keep Cards plays like a normal single elimination draft except that all the cards you draft are added to your collection. The prizes for winning a Keep Cards draft are 570 gold for first or 190 gold for second.
For most players Keep Cards is the best way to get new cards.