The Collaborative International Dictionary of English v.0.48:

Extinguishment \Ex*tin"guish*ment\, n.
   1. The act of extinguishing, putting out, or quenching, or
      the state of being extinguished; extinction; suppression;
      destruction; nullification; as, the extinguishment of fire
      or flame, of discord, enmity, or jealousy, or of love or
      affection.
      [1913 Webster]

   2. (Law) The annihilation or extinction of a right or
      obligation. --Abbott.
      [1913 Webster]

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

EXTINGUISHMENT, contracts. The destruction of a right or contract, the act
by which a contract is made void.
     2. Art extinguishment may be by matter of fact and by matter of law. 1.
It is by matter of fact either express, as when one receives satisfaction
and full payment of a debt, and the creditor releases the debtor 11 John.
513'; or implied, as when a person hath a yearly rent out of, lands and
becomes owner either by descent or purchase, of the estate subject to the
payment of the rent, the latter is extinguished 3 Stew. 60; but the person
must have as high an estate in the land as in the rent, or the rent will not
be extinct. Co. Litt. 147. See Merger.
     3. There are numerous cases where the claim is extinguished b operation
of law; for example, where two persons are jointly, but not severally
liable, for a simple contract debt, a judgment obtained against one is at
common law an extinguishment of the claim on the other debtor. Pet. C. C.
301; see 2 John. 213. Vide, generally, Bouv. Inst. Index, h.t.; 2 Root,
492; 3 Conn. 62; 1 Hamm. 187; 11 John. 513; 4 Conn. 428; 6 Conn. 373; 1
Halst. 190 4 N. H. Rep. 251 Co. Litt. 147 b; 1 Roll. Ab. 933 7 Vin. Ab. 367;
11 Vin. Ab. 461; 18 Vin. Ab. 493 to 515 3 Nels. Ab. 818; 14 Serg. & Rawle,
209; Bac. Ab. h.t.; 5 Whart. R. 541. Vide Discharge of a Debt.