Balanced means the each channel is made up of three separated entities: the positive signal, and its mirror image, the negative signal, plus a ground channel to complete the circuit. Since you have left and right channels, they add up to 6 entities together (though the grounds are shared, so 5 in total actually).
Single ended means the normal way of wiring that you will find on most source, like radio, iPod, etc. It only has a left channel, a right channel, and a shared ground.
Basically that means your audio interface has a different way of outputting signal, and therefore shouldn't be plugged directly into any normal 'single ended' headphone amp without knowing what might happen. If you are lucky, all you need is a custom made cable with the right wiring.
Anyway, just send an email to the manufacturer with this question:
Audio interface: I have model XXX, I want to connect the balanced line-out to a single ended headphone amp. Is it okay to feed the negative signal to the ground or should I leave it floating?
amp: I am interested in model XXX, but I am planning to feed it with an audio interface with balanced line-out, Is it okay to feed the negative signal to the ground or should I leave it floating?