Here's just a small explanation below, but if you want a fuller version, take a look here.
A maker makes an order within an order book that can be fulfilled by someone else later on. As a result, makers are the best users an exchange can have, as they provide the platform with liquidity and “make” the market.
The maker fee is the percentage of the order charged by the exchange to the maker at trade execution. A taker will take an order from an order book, therefore consuming or removing the liquidity it once offered. This happens when a user makes an order that is instantly matched by another order on the order book.
The taker fee is the percentage of the order charged by the exchange to the taker at trade execution.