A taker is an individual who accepts already available offer in the order book.
For instance, if you see an order to buy 1.0 BTC at some price, and you sell into that order, you will be the taker. In other words, you “took” the available offer. The counterparty will be the maker, as it “made” that offer and it was “taken”.
Exchanges usually impose higher fees on takers. Such practice encourages market participants to try to execute their trades as makers. When there’s an incentive to be a maker, the order book gets more liquid.