In every token trade, there are two parties to a transaction: the “Maker”, who posts orders on the order book, and the “Taker”, who fills the posted order. Takers by matching Makers' orders or in other words by “taking” a Makers order, complete or as we say fill the trade.
The Maker-Taker model encourages market liquidity in the relayer network by rewarding the Makers of that liquidity with a fee discount. Takers benefit from a tighter market spread due to the increased incentive for Makers to outbid each other. The higher fee the Taker pays should usually be offset by the better prices this tighter spread provides. All in all a more efficient low fee market model.