Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The process of approximating a continuous signal by a set of discrete symbols or integer values.
 n. A procedure for constructing a quantum field theory starting from a classical field theory.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the act of dividing into quanta or expressing in terms of quantum theory
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

Also the bare eye could see that the quantization was at least 1% accurate, and there was no reason it should have been even that good unless it was von Klitzing's effect.

Higher sampling rates are used because we can afford to do it now, and the higher sampling rates allow lower levels of certain complex aliasing (from amplitude quantization).

It began with Dirac's quantization of fields using the variables of amplitude and phase.

This problem is often known as “the quantization of gravity”.
Compactification in String Theory Part I: Motivation « Imaginary Potential

Now, in some sense, the quantization of gravity is an extremely academic (and masturbatory [that's now 2 blog posts, 1 powerpoint presentation!]) problem.
Compactification in String Theory Part I: Motivation « Imaginary Potential

The zero point energy of the quantum vacuum results from a quantization condition on harmonic oscillators.
Supermassive Black Holes Spinning Backwards Create Death Ray Jets?  Universe Today

Back to Ch. 33.7 (p. 983), where Penrose implements canonical quantization for twistors.

Subsequent chapters deal with the consequences of this quantization.

Instead, he applies the standard quantization procedure to twistor theory, the same canonical quantization that has been previously applied to nonrelativistic particles, spin, Maxwell's electromagnetic field and strings.

One needs, at the very least, to know quantum mechanics at the level of a twosemester undergraduate course: canonical quantization, operators, wave functions, that sort of things.
thebighenry commented on the word quantization
Quantization (linguistics)
In linguistics, a quantized expression is such that, whenever it is true of some entity, it is not true of any proper subparts of that entity. Example: If something is an "apple", then no proper subpart of that thing is an "apple". If something is "water", then many of its subparts will also be "water". Hence, "apple" is quantized, while "water" is not. Quantization has proven relevant to the proper characterization of grammatical telicity (roughly, sentences that present events as bounded/unbounded in time) and the mass/count distinction for nouns. The notion was first applied to linguistic semantics by the logician Manfred Krifka.
June 8, 2008