A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.
Matrices are rectangular arrays of numbers. A major application of matrices is to represent linear transformations:
A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a matrix and every matrix corresponds to a unique linear transformation. The matrix, and its close relative the determinant, are extremely important concepts in linear algebra and were first formulated by Sylvester (1851) and Cayley.
Excerpt reference: Wikipedia (adapted).