Suppose that you regress wage on years of education, but lack an ability variable to include in the regression. People with higher ability will earn more than others with the same years of education, so they will tend to have high positive error terms; but because they have higher ability they may find it easier (or more fun) to spend additional time in school. This creates correlation between the error term and the explanatory variable years of education, so the schooling coefficient will pick up both the fact that schooling makes you more productive (which is what you want), but also some of the effect of ability (which you don't want).