Ordered trees are the binary tree having some labels on the nodes.
Consider 2 nodes.
For unordered trees, you can make only two structure of trees.
(Root + left child) or (Root + right child)
Now consider Ordered trees case,
Suppose we label nodes as A,B.
Now in the two possible structures we can put A and B in 4 ways.
1. A(root) + B(left child)
2. A(root) + B ( right child)
3. B(root) + A( left child)
4. B(root) + A(right child)
I hope got the difference.