They are basically food particles that have got trapped in the tonsillar crypts(pits). This food has got partially digested and over time rots and salivary
calcium has deposited on it. They are called Tonsilloliths or Tonsil Stones.
The only solution is LASER Assisted Cryptolysis, where about 3mm thickness of the surface of the tonsils are vaporised by the LASER beam.