Two things are correlated if they tend to vary together so that the more there is one, the more (or less) there is of the other. The Appendix L explains correlation in greater detail and I recommend you read that if you are not familiar with the concept. The basic idea is simple enough. Height is correlated with weight because taller people tend to weigh more. Grades are correlated with intelligence because smarter people tend to do better in school. Smoking is correlated with lung cancer because people who smoke tend to die early from lung cancer. Whether you call it that or not, you are undoubtedly familiar with many natural correlations.
In many cases, scientists cannot use the experimental method because of practical or ethical limitations. Suppose, for example, that I wanted to find out if marijuana impairs learning ability. To do an experiment would be not be legal and not possible because some people would not be willing to participate. As another example, suppose I wanted to find out if there are racial differences in basic learning ability. There is no way to do an experiment that insures that every thing except racial heritage is equal. In these and many other cases, the best one can do is look for a correlation.
There are two important scientific points about correlations. A correlation does not establish causality. The correlation may be due to some other causal factor. Nevertheless, a correlation is useful to make predictions. It makes no difference why the events are correlated, if they vary together, you can use one to predict the other.