At the center of each tooth is a soft tissue called pulp. Normally, this vulnerable area is protected by hard walls of enamel that block bacteria and other harmful substances from reaching the pulp. When that protective enamel is injured (by cavity, chipped tooth, or other trauma), the tissue can become infected. The area will then close itself off to prevent a spread of infection and, inside this enclosed area, pus will develop. This is an abscess. Isn't nature elaborate and wondrous?
Sure it is, until the infection is yours. It'll start with toothache, dull and throbbing or jolts of pain. Your gums may feel swollen or tender, it will be painful to chew, and you may develop hypersensitivity to hot and cold. If you allow the infection to advance, you can look forward to fever, nausea, and breath that tastes just as bad as it smells. Oh, the humanity...
GO TO THE DENTIST! And when you do, s/he'll ask you to describe the pain. Then s/he'll probably take an x-ray of the area to get a better idea of the size and nature of the abscess. The dentist will then perform the most sophisticated test of them all: s/he will take the handle side of one of their instruments and will tap lightly (toward the gum) on the teeth in the area. The tooth that makes you scream the loudest wins.
So what now? If the abscess isn't too severe, it may be treated with antibiotics and something for the pain. To preserve the tooth, dentists frequently opt to perform a root canal, where they go into the area and remove the pulp (as well as any infection). Waiting too long to treat a tooth abscess can spread the infection or result in complete loss of the tooth, so once again: if you get a toothache, don't procrastinate and hope for the best. GO TO THE DENTIST!