Maker orders create (make) liquidity on a market by being entered onto the order book. Maker orders are not filled when they are placed, but instead, wait until a future order is placed that matches it. A maker order can be on either a buy or sell order. When an existing order on the order book is matched with a newly placed order (the taker), it charges the maker order in the transaction the maker fee.
Taker orders reduce (take away) liquidity on a market. Taker orders execute immediately and take volume off the order book. A taker order can be on either a buy or sell order. When a new order is placed and it matches against another order already on the order book (the maker), the taker in the transaction is charged the taker fee.