When trades on your order execute, fees are charged by CoinJax. Depending on how the trade executes, different fees apply. (See: Fee schedule)
"Taker" trades are defined as trades that execute upon orders that are existing on the order book. These trades execute immediately upon placing the order. Therefore, market orders are always "takers".
"Maker" trades are defined as trades that are taken. In other words, your order is placed on the order book. Then at a later time, someone else buys/sells against it.
Example
Someone has placed an LIMIT order SELLING 1 Bitcoin for 4000 USDT waiting for buyers. You then place an order to BUY 1 Bitcoin for 4000 USDT and trades happen between you and the seller. The seller will be considered a "maker" and you will be considered a "taker".
Partial filled orders
When you place an order, it may be partially filled immediately. The trades that happen immediately are "taker" trades as defined above. The remaining portion of the order will appear on the order book and any of your trades that execute here on will be considered "maker" trades.
To incentivise more orders to appear on the order book, CoinJax adopts lower trade fees for makers.