Reduced row echelon form is how a matrix will look when it is used to solve a system of linear equations.
Here is a system: x - y - 2z = 4
2x - y - z = 2
2x +y +4z = 16
The command on my TI-nspire is "rref" for reduced row echelon form. Enter the coefficients of the first equation from left to right, followed by the constant...then repeat for each equation in the system.
The solution to the system is: (24, 72, -26) as shown in the right hand column of the reduced matrix. That means that x = 24, y = 72, and z = -26.
Here is another example:
3x + 2y = 12
4x - y = 5
The solutions are x = 2 and y = 3!
If you need to know HOW to perform reduced row echelon form yourself (without a calculator), ask for a different explanation, or seek a video about Gauss-Jordan elimination... have fun solving systems!