Barrel
The part of the gun that the bullet travels through after it leaves the shell and before it leaves the gun. Most hand guns have barrels between 2 and 6 inches in length and between .22 and .5 inches in (internal) diameter.
Battery
In general, the term battery simply refers to the position of readiness of a gun for firing.
A semi-automatic is said to be “out of battery” when the slide is retracted enough to prevent the firing pin from striking the primer (thus preventing the gun from firing).
Failure to return to battery is a fairly common mode of failure for semi-automatics. Causes for semi-automatics failing to return to battery during normal operation include underlubrication and weak springs. This problem is usually easily fixed by a competent armorer.
Breech
The part of a firearm at the rear of the barrel. Generally, this is where the firing pin strikes the cartridge.
Bullet
The part of the cartridge that is actually propelled out of the firearm. Although people frequently use the term bullet when referring to the entire cartridge, this is not strictly correct. The bullet is just the part that is fired.