Correlations are useful for describing simple relationships among data. For example, imagine that you are looking at a dataset of campsites in a mountain park. You want to know whether there is a relationship between the elevation of the campsite (how high up the mountain it is), and the average high temperature in the summer.
For each individual campsite, you have two measures: elevation and temperature. When you compare these two variables across your sample with a correlation, you can find a linear relationship: as elevation increases, the temperature drops. They are negatively correlated.