A tricky way to sing. Rather than strictly follow the time, you sing in a more conversational manner, taking the beat as a suggestion rather than a rule.

If you can do this well, then you will sound very natural and intimate. If you do this poorly, it will sound like you have no idea how to sing.

Karen Carpenter and Frank Sinatra are generally acknowledged as being masters of vocal phrasing. The best way to see this is try try and sing along with them, and you'll see that even though they sound natural, they don't really follow the beat at all.