Source : Webster's Revised Unabridged Dictionary (1913)

Intelligibility \In*tel`li*gi*bil"i*ty\, [Cf. F.
   intelligilibilit['e].]
   The quality or state of being intelligible; clearness;
   perspicuity; definiteness.

Source : WordNet®

intelligibility
     n : the quality of language that is comprehensible [ant: {unintelligibility}]