Block Multiplication

Can someone explain "block multiplication" to me? It's not in the book, except in the context of a question as follows:

So the rule is that Matrix [A B] * colum matrix [C D] = [AC+BD] And I am supposed to verify it. but can I just ask how I would go about doing that since I really don't know what block multiplication does or what I'm supposed to multiply? Thanks.

Verify it by showing it gives the same answer as the standard definition of matrix multiplication. Write A as an array of scalars $a_{ij}$ and so on.