There are two compartments in a glow stick. The outer compartment holds dye and a chemical called diphenyl oxalate, and the inner glass vial hold hydrogen peroxide. When you crack the stick (and shake it up to mix the chemicals), the peroxide reacts with the diphenyl oxalate. This breaks down diphenyl oxalate into phenol (which doesn't do anything else) and a molecule named 1,2-dioxetanedione. Dioxetanedione is very unstable and breaks down spontaneously, at a relatively constant rate. When it breaks down, it releases energy. This energy excites the dye molecules, causing them to release light. The design of these is pretty ingenious - dioxetanedione is unstable, but diphenyl oxalate is very stable, so it will keep for a long time until it is exposed to the peroxide and the reaction starts. The rate at which dioxetanedione is constant, so there is a long-lasting, consistent light until it is all used up.

Because the light is produced by a chemical reaction, you can speed it up by heating the stick (this causes the molecules to move and interact more quickly, so the diphenyl oxalate breaks down faster). When you speed it up, the light is brighter but the chemicals are used up faster. Likewise, you can slow the reactions down (and make the light dimmer but last longer) with cold.

Glow sticks are also called "cyalume" sticks, because cyalume is the trademarked name for diphenyl oxalate.

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glowstick

p.s. if you want to play with heating and cooling glow sticks, be careful - they can melt, and microwaving one would be a very bad idea.