A bullet's caliber is a measure of its diameter. Specifically, it is a measure the projectile part, or slug, not the outer casing. Caliber is the measurement in millimeters, or hundredths or thousandths of an inch. Thus, a 22-caliber bullet is 0.22 inches in diameter.
Although the caliber designation seems very cut-and-dry when defined as a simple measurement, determining which caliber bullet to use with a particular gun can be quite confusing. For example, a 38 Special uses .357 caliber bullets.
A .30-06, or "thirty ought six" round is 0.30 caliber, manufactured according to the 1906 Army standard. The .30-30 is a bullet 0.30 inches in diameter, with 30 grains of powder. The rounds are different lengths as well, with the .30-06 being 7.62 millimeters by 63 millimeters, and the .30-30 being only 51 millimeters long.