Matrices are especially common when dealing with geometry. For example, rotating a point by 30 degrees and then moving it by 2 in the x-direction can be encoded as a single 3x3 matrix. You then multiply a point with that matrix to get your answer.
If you are rendering a 3D world you eventually have to get it onto your 2D screen and one way to do it is to do a bunch of matrix operations to flatten the scene to 2D.
You can also use them to solve linear equations or do all sorts of statistical things.
Matrices are a concept taken from mathematics, so you will encounter them when programming mathematical things. They are surprisingly general and they pop up everywhere.