The Collaborative International Dictionary of English v.0.48:

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.
   [1913 Webster]

WordNet (r) 3.0 (2006):

soffit
    n 1: the underside of a part of a building (such as an arch or
         overhang or beam etc.)