A simplistic example demonstrates the principle
Suppose all cars can be classified as either big or small, and can also be classified as loud or quiet. Suppose that 50% of cars are big (and hence 50% are small). Suppose also that 50% of cars are loud (and hence 50% are quiet).
Suppose that we looked at just the loud cars, and measured how many of them are big. If 50% of them are big, there is no correlation (loud cars are just as likely as quiet cars to be big). If 95% of them are big there is a strong correlation. In this case loud cars are more likely to be big that quiet cars. A correlation of zero means no correlation. A correlation of one means that the correlation is complete (ie that all loud cars are big).
How is this useful? It allows us to predict behavior. If 95% of loud cars are big, then if we hear a loud car, we guess that it is a big car, and be right most of the time. It does not allow us to be right all the time, but it allows us to be right more often than if we had not spotted the pattern.
There is no mechanism here for answering the question of why loud cars tend to be big - just for noticing the patterns.
Significantly too, just because we have spotted a predictor does not mean there is a causal link between the two. To suggest that we have shown that cars being big causes them to be loud is silly, as is the suggestion than we have shown that cars being loud causes them to be big. In fact one may be true, both may be true, or they may both may be causally linked to a third factor (like being driven by morons).
Other difficulties come too, when we try to apply these predictors to people.
Suppose you lend lots of people money. Some pay it back, and some don't. You keep records on these people, and you notice that 95% of brown-eyed people pay you back, but only 10% of blue-eyed people pay you back.
What do you do? Is it acceptable to exclusively lend money to brown-eyed people after that? Is it acceptable to insist on a higher level of security for blue-eyed people? To do so would be discriminatory.
Suppose you dated lots of people and found that blonde haired people made better partners than non-blonde people. You decide to exclusively date blonde-haired people.
Few non-Caucasian people are blonde (ie there is a correlation between hair color and race). So does it make you racist?
A popular strategy of the politically correct is to try to control debate by dictating what can and cannot be correlated.
See