For every trade, there is a maker and a taker. The maker is the one creating the initial order (a buy or a sell order), thereby making the order in the order book. The taker is the one buying or selling to that initial order, thereby taking it off the order book.
For example, you place a buy order of 1 BTC at 300,000 THB. After one minute, someone sells 1 BTC to you for 300,000 THB and your order is completely filled. The fee you owe is called a maker fee and the fee the other person owes is the taker fee. Free maker fees mean you can place as many limit orders as you want (i.e., buy orders below market price and sell orders above market price) and not pay any fees when your orders are matched.