The Collaborative International Dictionary of English v.0.48:

Mesne \Mesne\, a. [Cf. Mean intermediate.] (Law)
   Middle; intervening; as, a mesne lord, that is, a lord who
   holds land of a superior, but grants a part of it to another
   person, in which case he is a tenant to the superior, but
   lord or superior to the second grantee, and hence is called
   the mesne lord.
   [1913 Webster]

   Mesne process, intermediate process; process intervening
      between the beginning and end of a suit, sometimes
      understood to be the whole process preceding the
      execution. --Blackstone. --Burrill.

   Mesne profits, profits of premises during the time the
      owner has been wrongfully kept out of the possession of
      his estate. --Burrill.
      [1913 Webster] Meso

Bouvier's Law Dictionary, Revised 6th Ed (1856):

MESNE PROFITS, torts, remedies. The value of the premises, recovered in
ejectment, during the time that the lessor of the plaintiff has been
illegally kept out of the possession of his estate by the defendant; such
are properly recovered by an action of trespass, quare clausum fregit, after
a recovery in ejectment. 11 Serg. & Rawle, 55; Bac. Ab. Ejectment, H; 3 Bl.
Com. 205.
     2. As a general rule, the plaintiff is entitled to recover for such
time as be can prove the defendant to have been in possession, provided he
does not go back beyond six years, for in that case, the defendant may plead
the statute of limitations. 3 Yeates' R, 13; B. N. P. 88.
     3. The value of improvements made by the defendant, may be set off
against a claim for mesne profits, but profits before the demise laid,
should be first deducted from the value of the improvement's. 2 W. C. C. R.
165. Vide, generally, Bac. Ab. Ejectment, H; Woodf. L. & T. ch. 14, s. 3; 2
Sell. Pr. 140; Fonb. Eq. Index, h.t.; Com. L & T. Index, h.t.; 2 Phil. Ev.
208; Adams on Ej. ch. 13; Dane's Ab. Index, h.t.; Pow. Mortg. Index, h.t.;
Bouv. Inst. Index, h.t.