Caliber

Caliber is a diameter measurement of a bullet in inches.  Therefore a .22 caliber has a diameter that is 22/100 of an inch.  The caliber only refers to the size of the slug and not the size of the bullets casing (see pictures below).

A 8mm (.32 cal) Rifle Casing

A 8mm (.32 cal) Slug

Caliber has a good deal to do with a bullets effectiveness.  Larger calibers are often heavier and thus carry more energy.  Not only do larger calibers have more energy, they have a larger surface area upon impact, dealing a more effective transfer of energy.  This is often referred to as "stopping power."