A matrix A is said to be in reduced row echelon form iff:
a) every leading non-zero entry is to the right of the leading non-zero entry in the row above.
b) every leading entry in each non-zero row is equal to one.
c) in every column with a pivot, the pivot is the only non-zero entry in that column.
d) all zero rows are grouped at the bottom of the matrix.

An example of a matrix in reduced row echelon form(RREF):
|1 0 0 0|
|0 1 0 0|
|0 0 0 0|
|0 0 0 0|

The rank of a matrix is the number of rows in the RREF of the matrix. In the example the rank of the matrix is 2.