A matrix is a rectangular or tabular representation of quantities. Like a table, it has rows and columns and each "cell" is called an element. Matrices can be combined using addition, subtraction or multiplication, provided certain rules are followed about the sizes of the matrices involved.
A matrix is a shorthand form of an expression that could consist of elements added together if written out in full. The advantage of using this shorthand form is that matrices can be used to solve problems, sometimes complex, that would be more tedious and difficult to solve using a "longhand" approach. There are rules that determine how matrices can be added, subtracted or multiplied, and matrices occupy a complete branch of mathematics of their own.
The given matrix is a 1 by 4 matrix (one row and 4 columns) and it could represent the longhand:
w+5x+4y+z (for example), where w, x, y, z are variables and the numbers are coefficients. But it could represent a 4-dimensional vector (a difficult concept to visualise) which is involved with other similar matrices representing vectors to solve a problem using vector analysis. Matrices are used in many branches of science to solve quite difficult physical problems.