The Collaborative International Dictionary of English v.0.48:

Quantum \Quan"tum\, n.; pl. Quanta. [L., neuter of quantus how
   great, how much. See Quantity,]
   1. Quantity; amount. "Without authenticating . . . the
      quantum of the charges." --Burke.
      [1913 Webster]

   2. (Math.) A definite portion of a manifoldness, limited by a
      mark or by a boundary. --W. K. Clifford.
      [1913 Webster]

   Quantum meruit[L., as much as he merited] (Law), a count in
      an action grounded on a promise that the defendant would
      pay to the plaintiff for his service as much as he should
      deserve.

   Quantum sufficit, or Quantum suff. [L., as much suffices]
      (Med.), a sufficient quantity; -- abbreviated q. s. in
      pharmacy.

   Quantum valebat[L., as much at it was worth] (Law), a count
      in an action to recover of the defendant, for goods sold,
      as much as they were worth. --Blackstone.
      [1913 Webster]

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

QUANTUM MERUIT, pleading. As much as he has deserved. When a person employs
another to do work for him, without any agreement as to his compensation,
the law implies a promise from, the employer to the workman that he will pay
him for his services, as much as be may deserve or merit. In such case the
plaintiff may suggest in his declaration that the defendant promised to pay
him as much as he reasonably deserved, and then aver that his trouble was
worth such a sum of money, which the defendant has omitted to pay. This is
called an assumpsit on a quantum meruit. 2 Bl. Com. 162, 3 1 Vin. Ab. 346; 2
Phil. Ev. 82.
     2. When there is an express contract for a stipulated amount and mode
of compensation for services, the plaintiff cannot abandon the contract and
resort to an action for a quantum meruit on an implied assumpsit. 18 John.
R. 169; 14 John. R. 326; 10 Serg. & Rawle, 236. Sed vide 7 Cranch, 299;
Stark. R. 277; S., C. Holt's N. P. 236; 10 John. Rep. 36; 12 John. R. 374;
13 John. R. 56, 94, 359; 14 John. R. 326; 5 M. & W. 114; 4 C. & P. 93; 4 Sc.
N. S. 374; 4 Taunt. 475; 1 Ad. & E. 333; Addis. on Contr. 214.