For me it's a massive increase in my interest in sex, and also a massive shift in risk taking sexual behaviour. When I'm euthymic, I probably have a slightly lower than normal sex drive and I'm only interested in my wife (soon to be ex).
If the hyper-sexuality is there then I'm looking for anyone and everyone to sleep with and have hooked up with many women and couples that I've met online and offline. I also start looking at increasingly risky material online that I would otherwise be repulsed by, but if the hyper-sexuality's there then it's fair game. To me it's like living in a world with no consequences and any behaviour is acceptable.
Unfortunately the risk taking element of hyper-sexuality can be incredibly destructive as I have found out first hand. I have the bad luck of being afflicted with extreme hyper-sexuality and exorbitant spending when manic/hypomanic.
Unfortunately the hyper-sexuality has gotten me into serious legal trouble, although it was also the catalyst for me getting my diagnosis last year.
My advice is to speak to a pdoc if you're even slightly concerned about your sexual behaviour, try and get on top of it before it becomes destructive.