Simple Definition:

A matrix is a rectangular arrangement of numbers, symbols, or expressions, called elements, in rows and columns. The elements of a matrix can be real numbers, complex numbers, or any other mathematical object. Each element in a matrix has a specific address, called its row and column position.

For example,

[2  3  4]
[1  5  6]

is a matrix with 2 rows and 3 columns.

Very Simple Definition:

A matrix is a table of numbers or symbols arranged in rows and columns.

For example,

1   2   3
4   5   6

is a matrix with 2 rows and 3 columns.