The Collaborative International Dictionary of English v.0.48:

Branchial \Bran"chi*al\, a. (Anat.)
   Of or pertaining to branchi[ae] or gills.
   [1913 Webster]

   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.
      [1913 Webster]