The Collaborative International Dictionary of English v.0.48:

Mesquite \Mes*qui"te\ (m[e^]s*k[=e]"t[asl]), Mesquit \Mes*quit"\
   (m[e^]s*k[=e]t"), n. [Sp. mezquite; said to be a Mexican
   Indian word.] (Bot.)
   Aany of several small spiny trees or shrubs of the
   southwestern part of North America belonging to the genus
   Prosopis having small flowers in axillary cylindrical
   spikes followed by large sugar-rich pods, especially the
   honey mesquite, and screw-pod mesquite.
   [1913 Webster + WordNet 1.5]

   Honey mesquite. See Algaroba
   (b) .

   Screw-pod mesquite, a smaller tree (Prosopis pubescens),
      having spiral pods used as fodder and sometimes as food by
      the Indians.

   Mesquite grass, a rich native grass in Western Texas
      (Bouteloua oligostachya, and other species); -- so
      called from its growing in company with the mesquite tree;
      -- called also muskit grass, grama grass.
      [1913 Webster]

WordNet (r) 3.0 (2006):

honey mesquite
    n 1: thorny deep-rooted drought-resistant shrub native to
         southwestern United States and Mexico bearing pods rich in
         sugar and important as livestock feed; tends to form
         extensive thickets [syn: honey mesquite, Western honey
         mesquite, Prosopis glandulosa]