Row Echelon Form (REF) is a specific arrangement of a matrix used in linear algebra. In this form, all non-zero rows are above any rows of all zeros, and the leading coefficient (or pivot) of each non-zero row is to the right of the leading coefficient of the previous row. This structure helps in solving systems of linear equations. To achieve Row Echelon Form, one typically uses Gaussian elimination, a method that involves row operations to simplify the matrix. REF is a crucial step in finding solutions to linear systems, as it makes it easier to perform back substitution to find the values of the variables.