When you pass a dump, you might hold your nose and say, "Oh, I can't handle the stench." A stench is a bad smell.
Stench can also be used metaphorically. If it is discovered that many members of a police force have been taking money from mob bosses so that they can continue their life of crime, a new chief may be brought in to remove the stench of corruption from the office. In either sense, stench is the kind of smell that takes work to get rid of.