The Collaborative International Dictionary of English v.0.48:

Averment \A*ver"ment\, n. [Cf. OF. averement, LL. averamentum.
   See Aver, v. t.]
   1. The act of averring, or that which is averred;
      affirmation; positive assertion.
      [1913 Webster]

            Signally has this averment received illustration in
            the course of recent events.          --I. Taylor.
      [1913 Webster]

   2. Verification; establishment by evidence. --Bacon.
      [1913 Webster]

   3. (Law) A positive statement of facts; an allegation; an
      offer to justify or prove what is alleged.
      [1913 Webster]

   Note: In any stage of pleadings, when either party advances
         new matter, he avers it to be true, by using this form
         of words: "and this he is ready to verify." This was
         formerly called an averment. It modern pleading, it is
         termed a verification. --Blackstone.
         [1913 Webster] Avernal

WordNet (r) 3.0 (2006):

averment
    n 1: a declaration that is made emphatically (as if no
         supporting evidence were necessary) [syn: assertion,
         averment, asseveration]

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

AVERMENT, pleading. Comes from the Latin verificare, or the French averrer,
and signifies a positive statement of facts in opposition to argument or
inference. Cowp. 683, 684.
     2. Lord Coke says averments are two-fold, namely, general and
particular. A general averment is that which is at the conclusion of an
offer to make good or prove whole pleas containing new affirmative matter,
but this sort of averment only applies to pleas, replications, or subsequent
pleadings for counts and a vowries which are in the nature of counts, need
not be averred, the form of such averment being et hoc paratus. est
verificare.
     3. Particular averments are assertions of the truth of particular
facts, as the life of tenant or of tenant in tail is averred: and, in these,
says Lord Coke, et hoc, &c., are not used. Co. Litt. 362 b. Again, in a
particular averment the party merely protests and avows the truth of the
fact or facts averred, but in general averments he makes an offer to prove
and make good by evidence what he asserts.
     4. Averments were formerly divided into immaterial and impertinent; but
these terms are now treated as synonymous. 3 D. & R. 209. A better division
may be made of immaterial or impertinent averments, which are those which
need not be stated, and, if stated, need not be proved; and unnecessary
averments, which consist of matters which need not be alleged, but if
alleged, must be proved. For example, in an action of assumpsit, upon a
warranty on the sale of goods, allegation of deceit on the part of the
seller is impertinent, and need not be proved. 2 East, 446; 17 John. 92. But
if in an action by a lessor against his tenant, for negligently keeping his
fire, a demise for seven years be alleged, and the proof be a lease at will
only, it will be a fatal variance; for though an allegation of tenancy
generally would have been sufficient, yet having unnecessarily qualified it,
by stating the precise term, it must be proved as laid. Carth. 202.
     5. Averments must contain not only matter, but form. General averments
are always in the same form. The most common form of making particular
averments is in express and direct words, for example: And the party avers
or in fact saith, or although, or because, or with this that, or being, &c.
But they need not be in these words, for any words which necessarily imply
the matter intended to be averred are sufficient. See, in general, 3 Vin.
Abr. 357 Bac. Abr. Pleas, B 4 Com. Dig. Pleader, C 50, C 67, 68, 69, 70; 1
Saund. 235 a, n. 8 3 Saund. 352, n. 3; 1 Chit. Pl. 308; Arch. Civ. Pl. 163;
Doct. Pl. 120; 1 Lilly's Reg.  209 United States Dig. Pleading II (c); 3
Bouv. Inst. n. 2835-40.