Taker:
When you place an order that trades immediately, by filling partially or fully, before going on the order book, those trades will be "taker" trades.
Trades from Market orders are always takers, as market orders can never go on the order book. These trades are "taking" volume off of the order book, and are therefore called the "taker".
Maker:
When you place an order that goes on the order book partially or fully (such as a limit order placed via the trading screen), any subsequent trades coming from that order will be as a “maker”.
These orders add volume to the order book, helping to "make the market", and are therefore termed the "maker" for any subsequent trades.