An auction mechanic usually involves players competing by bidding against one another ti enhance your position within the game. Bidding usually involves a currency and can be undertaken in a few ways:
The first is sealed bids where all players would tender their offers at the same time with the highest bidder winning.
The second is the Japan style bidding system where all players bid for an item but if they pass a bid they cannot reenter the battle.
There are other ways of bidding, such as a Dutch auction, but the above two are the most common used in board games.