A Jordan block with value λ is a square, upper triangular matrix whose entries are all λ on the diagonal, 1 on the entries immediately above the diagonal, and 0 elsewhere.
Typical Jordan blocks of size 1, 2, and 3 look like the following:
A Jordan form matrix is a block diagonal matrix whose blocks are all Jordan blocks. For example, the following matrices are all Jordan form matrices:
In the first matrix among the preceding set of matrices, we should notice that the block on the top left [[1,1],[0,1]] is a Jordan block of size 2, while the matrix on the bottom right is a Jordan block of size 1.