A stereotype is a generalization or assumption about a group of people based on perceptions of the group's traits. Stereotypes can be positive (as in, "all members of Group X are smart and successful"), but are most often negative (as in, "all members of Race Y are lazy").
Regardless of the "positive" or "negative" nature of the stereotype, the problem with stereotyping is that it has the practical effect of forcing one's own perceptions of a group onto its members, who will not all share the trait being imputed to them. Negative stereotypes can be damaging.
Many outside the United States have a stereotype that all Americans are wealthy. While many Americans are rich, particularly compared to the rest of the world, by no means are all Americans wealthy. Seung-Hui Cho murdered 32 people at Virginia Tech based in part of his stereotype of them as "rich kids," when many were not.
Political correctness is an attempt to ban all stereotypes from speech, even stereotypes useful to guard against danger. For example, political correctness opposes any type of profiling based on national origin or religion, even if the profiling would make it easier to screen and stop terrorism. Under this view, airports must consider an 80-year-old nun to be as likely to be a terrorist as a group of 20-year-old male radicals.
Psychologists have shown that stereotypes are nonetheless helpful for human beings - it helps cut down on the information to be processed if the brain can make assumptions about a person upon first meeting, thus preserving processing power. As a result, stereotyping is unlikely to disappear.