This can be completely painless, or only give a very slight dull ache from time to time.
There is a swelling or a lump under the tooth, which may or may not be oozing pus.
This can either be caused by an infection from within the tooth, or from within the gums.
Infections from within the tooth usually occur when bacteria manages to enter the nerve space in the middle of the tooth. Pus forms within the tooth, and then leaks out through the base of the tooth and drains out from the little lump.
Infections from within the gums usually occur when too much tartar/calculus builds up, trapping bacteria and debris under the gums. This causes the gums to get infected and swell up very severely.
If the source of infection is within the tooth, and the tooth is not too heavily damaged, the infection can be drained out by performing a root canal treatment.
If the source of infection is from within the gums, the tartar/calculus which is trapping the bacteria inside needs to be removed, and the area under the gums flushed out.
The infection can continue to spread, causing the face the get swollen. In very severe cases, the swelling can be big enough to affect other areas, such as the throat. This can be dangerous and potentially result in hospitalisation.