It usually means "we want you to play with our band exclusively". Which is, of course, pure nonsense. When a band can keep me gigging and making as much money as I think I could/should be making at it, I can commit. In the meantime, I'll play with whomever, wherever, and as often as I please. That "commitment" crap wore thin with me ... 30 years in the corporate jungle, and all it got me was a forced retirement about five years before I wanted to retire. I now do what's right for ME ... it may include you, but maybe not.
That's fine, but then I'll pay you as a hired-gun, which means a flat rate, regardless of actual gig revenue. So you may still only make market rate, even if it's a high paying gig. I also have no problem firing you if your moonlighting is causing the band to lose work.
I know two drummers who are constantly in and out of bands because they join and expect to be rockstars in two weeks. It's a shame, because they're both ubertalented. One's Berklee-trained. But I wouldn't work with either them unless it was to hire them to sub for a gig or two.