Crypt
In anatomy, a crypt is variously a blind alley, a tube with no exit, a depression, or a pit -- in an otherwise fairly flat surface.</P> Cryptic in the case of the tonsils refer to the tonsillar crypts which are little pitlike depressions in the tonsils.</P> The words crypt and cryptic come from the Greek 'kryptos' meaning hidden or concealed.
Thus, cryptic tonsillitis may be hidden, concealed because it is down in the pits (of the tonsil).