What is causing this stain on my driveway?
BMitch is right on his comment.   This probably wasn't "dirt" but was some oil, rust, other chemicals...  When you paint over them you dry them out and the result is a chemical reaction with the paint/stain because you are drying the material out - it cannot access air - and it will try to escape through the stains you see.

I know this because I paint my laundry floor every 3-4 years and I sweep it well but really don't feel like giving it a good cleaning.  My fix is to just put more paint over it - which works sometimes on the first coat and sometimes 2-3 coats later.  Is the paint bonded as good as it could be?  No.  But it is a floor.   If you don't want to see these you have to do some serious cleaning before painting floors/driveways.