Let's decouple the various things in that sentence - and push DC coupling to the side.
But the balanced modulator and differential power stage are linked and relevant. A class-D (digital) amp is basically a big honkin' DAC that drives your speakers, with the speakers as part of the final low pass ("reconstruction") filter.
99% of amps are unbalanced which means that the power is created between oen speaker terminal ( the red one) and ground ( the black or green one). A balanced interface (regardless of whether it is low level interconnect or to the speaker) is differential with two mirror-image signals. The load (speaker in this case) sees + and - versions of the same thing. NEITHER is ground. While one is going high, say to +10V the other is going low to -10V. So, if you ground either one by mistake, you have shorted your amp. Since the speaker has no ground and is an insulated (wood) box, it floats. No issue.
You do need to ensure that you maintain proper polarity which can be more confusing - but i expect this amp is marked clearly.
So unless you are doing something unusual (bi amping for example) - not much to concern yourself with.
G