Matrices (the singular is matrix; plural is matrices, pronounced MAY-truh-sees) have many uses. For a good understanding of them, I strongly suggest you take a course in linear algebra (or do some searches for it online).

Matrices can be used to represent and solve systems of linear equations (look up Gaussian elimination), to represent linear transformations, and much more, and they have loads of applications in computer graphics (linear transformations), in encryption (e.g., look up the Hill cipher), in economics, in graph theory, in linear programming, in networks (such as traffic networks and electrical networks), and in many other areas.

Again, an elementary linear algebra class should give you the necessary foundation, as well as an indication of potential applications.