A correlation matrix is formed when you have multiple features on a stream or set of data, for example multiple database records or time series. The correlation cooefficient is calculated for each pair of features and set in a matrix. The matrix is symmetric as the correlation cooefficient does not depend on the order of the features, and the diagonal is the correlation between a feature and itself.
The correlation matrix can be used as a means to visualise the relationships between features, and in particular if there are some groups of features that are all closely related with one anther. It can also be used as a pre-processing step before other analysis such as clustering of features or dimensional reduction.