A taker order is when you place an order at the market price that gets filled immediately.
The taker term is used to identify someone who is taking out liquidity from the market and normally a higher fee is charged for that type of orders.
A maker order is when you place an order which is not immediately matched by an existing order, so it contributes to make liquidity in the market. Normally a lower fee is charged for this type of orders.
In Eidoo hybrid exchange you are not charged at all for maker orders.
Also, in case of partially executed taker orders you will be charged just for the first execution.