I wish you were more specific on what part you need help with.Wikipedia has an explanation that might help. The goal in Gaussian elimination is to make a lot of entries of the matrix zero. That way we can solve a system of linear equations, find the inverse or rank of a matrix much easier. The best way to understand it is to do a few problems. Wiki already has an example. Look at that and see if it helps. Wolfram also has an entry for that with an example. In summary you start with looking at the first column of the matrix and try to make all entries zero, except for the first entry. To do that you just add multiples of the first row to the other rows and make them all zero. Then you move to the next column and make the third, fourth, etc. entries of the second column zero. Then you go to the third column and make the fourth, fifth, etc. entries of this column zero. And so on. Let me know which part you don’t understand and I will try to help.