Source : Webster's Revised Unabridged Dictionary (1913)

Branchial \Bran"chi*al\, a. (Anat.)
   Of or pertaining to branchi[ae] or gills.

   {Branchial arches}, the bony or cartilaginous arches which
      support the gills on each side of the throat of fishes and
      amphibians. See Illustration in Appendix.

   {Branchial clefts}, the openings between the branchial arches
      through which water passes.

Source : WordNet®

branchial
     adj : of or relating to gills (or to parts of the body derived
           from embryonic gills)