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 therefore called the "taker."
Limit IOC and Limit FOK orders (accessible via the API) are also always Takers, for the same reason.
When you place an order that goes on the order book partially or fully (such as a limit order placed via the trading screen on binance.US), 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.
Note: It is possible for a Limit GTC order (accessible via the API) to have traded as the taker and maker.