Some subwoofers have double voice coil, what means you need the two outputs of the receiver (or a Y connector) to make it sound at its full potential (it won't sound better, only louder if you connect both inputs); and some subwoofers need only one cable because they have only one input.
Generally those inputs are indicated behind the subwoofer:
a) one input, might say: subwoofer (mono) line in or LFE INPUT. In this case, you don't need to connect both cables.
B) two inputs, might say: right-left inputs. In this case, you will need to connect both of them or use a Y connector.
c) Speaker inputs: to connect the sub in the old fashioned way, but, you will not have the LFE channel in multichannel music or movies.