Wires coming out of a pigtail cable
If you choose one wire or the other, you will only hear that channel, so some music will be noticeably different.  You can mix the two channels, or if you desire mono, getting a mono plug wouldn't hurt.  If you were attaching this to headphones, you could connect two headphones to one wire with the effects mentioned above, plus you might halve your volume and screw up impedance, possibly damaging amplifier outputs.

The ring and white wire are the right audio channel and the tip and red wire are the left audio channel.