Basically any old wet stains on wood, or drywall or plaster. Say you had some water damage but you fixed the leak, you can cover the stains with kilz or binz primers. They are called stain blockers. I find the oil based to work better than water based.
I also use it to cover darker paint on the walls. Lets say I have a red wall. I prime it with this primer and then when it dries I can paint the wall white and not end up with a pink wall.