white bits in the tonsils are usually accretions of solid pus that gather on bits of stuck food, the more crenellated your tonsils are, the more likely things will get stuck in there
they're called tonsil stones or tonsilliths
O I had them a couple of years back -was just like curdled cheese -im only posting to confirm what the others have said -its horrible -the bits just appear in your mouth.
Mine just disappeared after a few months and they havent returned -they-as in the cruddy bits lol !!
Just another confirmation. I get them sometimes too, maybe every 4 or 5 months or so. If you get them often, maybe gargling with a mouthwash or salt water may help.