When one you and a some friends go out clubbin'and one of them ends up getting S#!T faced and you end up watching them all night; cleaning up their puke, keeping them from hooking up with nastypeople/fighting people, helping them walk/up when they fall-thus ruining your entire evening and resluting in you not having any fun.
To watch your friend while they are wasted out of their mind and don't know what's going on.
"Dude, when you took those 69 hits of acid i had to babysit you for a week. You were out of your mind. I strapped you to the bed to keep you from running out into the street naked and killing the neighbors kids."
The above is a very extreme example of druggy babysitting.
The below is a more average level of babysitting....
When he went into the K-Hole it was up to his friends to babysit him and keep him from swallowing his tounge, vomit, and that he doesn't have snot all over his face.