Source : Webster's Revised Unabridged Dictionary (1913)

Soffit \Sof"fit\, n. [It. soffitta, soffitto, fr. soffiggere to
   hide, properly, to fix or fasten under, L. suffigere to
   fasten beneath or below; sub under, beneath + figere to fix,
   faste: cf. F. soffite.] (Arch.)
   The under side of the subordinate parts and members of
   buildings, such as staircases, entablatures, archways,
   cornices, or the like. See Illust. of {Lintel}.

Source : WordNet®

soffit
     n : the underside of a part of a building (such as an arch or
         overhang or beam etc.)