Some good points made already.
Some things to add:
I strongly prefer and advise people to use the spinning hammerfist rather than the spinning backfist. Hammerfists are generally much more durable/resistant to injury than backfists (provided you don't spin with the arm pre-straightened, in which case you are asking to get your elbow hyperextended) and lend themselves better to a spinning back elbow should the opponent unexpectedly close on you.
A couple good uses for the spinning hammer/backfist that I like are:
-after you miss a round kick and are spinning through to potentially catch someone coming in to counter you
-to "double up" a circular attack (I.e. Left hook to head right spinning hammerfist). Just like doubling up a jab the second striking has a good chance of landing
-after a jab/double jab which turns you "Side Stance" (also btw setting you up for a lead leg side kick/round kick/hook kick which can act as a good mix up), especially good if the stay just out of reach or try to parry/block the jab (and even if they try to return fire with their right cross)
-off of a shoulder roll against the straight right/right cross. This is especially true if they don't get their guard back immediately, and even then it can be a very powerful shot so they may still take some of it.