Gaussian Elimination is a mathematical method used to solve systems of linear equations. It transforms a given system into an equivalent one that is easier to solve by using a series of row operations on an augmented matrix. These operations include swapping rows, multiplying a row by a non-zero scalar, and adding or subtracting rows. The goal of Gaussian Elimination is to reach a form called row echelon form, where each leading coefficient (the first non-zero number from the left in a row) is to the right of the leading coefficient of the previous row. This simplification allows for straightforward back substitution to find the solution to the system.