The Collaborative International Dictionary of English v.0.48:

Affirmation \Af`fir*ma"tion\, n. [L. affirmatio: cf. F.
   affirmation.]
   1. Confirmation of anything established; ratification; as,
      the affirmation of a law. --Hooker.
      [1913 Webster]

   2. The act of affirming or asserting as true; assertion; --
      opposed to negation or denial.
      [1913 Webster]

   3. That which is asserted; an assertion; a positive
      statement; an averment; as, an affirmation, by the vender,
      of title to property sold, or of its quality.
      [1913 Webster]

   4. (Law) A solemn declaration made under the penalties of
      perjury, by persons who conscientiously decline taking an
      oath, which declaration is in law equivalent to an oath.
      --Bouvier.
      [1913 Webster]

WordNet (r) 3.0 (2006):

affirmation
    n 1: a statement asserting the existence or the truth of
         something [syn: avowal, avouchment, affirmation]
    2: the act of affirming or asserting or stating something [syn:
       affirmation, assertion, statement]
    3: (religion) a solemn declaration that serves the same purpose
       as an oath (if an oath is objectionable to the person on
       religious or ethical grounds)
    4: a judgment by a higher court that the judgment of a lower
       court was correct and should stand [ant: reversal]

Moby Thesaurus II by Grady Ward, 1.0:

162 Moby Thesaurus words for "affirmation":
   John Hancock, OK, Parthian shot, a priori principle, acceptance,
   accord, acquiescence, address, admission, affidavit, affirmance,
   affirmative, affirmative voice, agreement, allegation, answer,
   apostrophe, approbation, approval, apriorism, assent, assertion,
   asseveration, assumed position, assumption, attest, attestation,
   authentication, authorization, averment, avouchment, avowal, axiom,
   aye, backing, backing up, basis, bearing out, blessing, bolstering,
   buttressing, categorical proposition, certification,
   circumstantiation, comment, compliance, compurgation, confirmation,
   connivance, consent, corroboration, corroboratory evidence,
   countersignature, crack, data, declaration, deposition, dictum,
   disclosure, documentation, eagerness, endorsement, exclamation,
   expression, first principles, fortification, foundation, go-ahead,
   green light, greeting, ground, hypothesis, hypothesis ad hoc,
   imprimatur, instrument in proof, interjection, legal evidence,
   lemma, major premise, mention, minor premise, nod, notarization,
   notarized statement, note, observation, okay, permission,
   philosopheme, philosophical proposition, phrase, position,
   postulate, postulation, postulatum, premise, presupposition,
   profession, promptitude, promptness, pronouncement, proof,
   proposition, propositional function, proving, proving out,
   question, ratification, readiness, reflection, reinforcement,
   remark, rubber stamp, sanction, say, saying, seal, sentence, sigil,
   signature, signet, stamp, stamp of approval, statement,
   statement under oath, strengthening, subjoinder, submission,
   subscription, substantiation, sumption, support,
   supporting evidence, supposal, swearing, sworn evidence,
   sworn statement, sworn testimony, testimonial, testimonium,
   testimony, the nod, theorem, thesis, thought, truth table,
   truth-function, truth-value, undergirding, ungrudgingness,
   unloathness, unreluctance, utterance, validation, verification,
   visa, vise, vouching, warrant, willingness, witness, word



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

AFFIRMATION, practice. A solemn declaration and asseveration, which a
witness makes before an officer, competent to administer an oath in a like
case, to tell the truth, as if be had been sworn.
     2. In the United States, generally, all witnesses who declare
themselves conscientiously scrupulous against taking a corporal oath, are
permitted to make a solemn affirmation, and this in all cases, as well
criminal as civil.
     3. In England, laws have been enacted which partially relieve persons
who, have conscientious scruples against taking an oath, and authorize them
to make affirmation. In France, the laws which allow freedom of religious
opinion, have received the liberal construction that all persons are to be
sworn or affirmed according to the dictates of their consciences; and a
quaker's affirmation has been received and held of the same effect as an
oath. Merl. Quest. de Droit, mot Serment, Sec. 1.
     4. The form is to this effect: "You, A B, do solemnly, sincerely, and
truly declare and affirm," &c. For the violation of the truth in such case,
the witness is subject to the punishment of perjury as if he had been sworn.
     5. Affirmation also means confirming; as, an affirmative statute.