Wow! I hardly know where to begin. I devote an hour to SUMPRODUCT in
the "Excel for Financial Analysts" class I teach...and it usually runs into
overtime. Why? Because SUMPRODUCT is Excel's "duct tape" function....it
works when practically nothing else will.

First, see SUMPRODUCT in Excel Help.

Basically, that function multiplies two or more same sized ranges
...then, sums the resulting products.

Example:
A1:B3 contains these values
4 7
5 8
6 9

If you wanted to multiply Col_A x Col_B, you'd get:
4 7 =28
5 8 =40
6 9 =54

The sum of those products is: 122

The SUMPRODUCT function, in this form, does exactly that:
=SUMPRODUCT(A1:A3,B1:B3)
=122

It also works in this form:
=SUMPRODUCT((A1:A3)*(B1:B3))
=122

Now, here's the fun part....You can put Boolean Expressions (fancy term for
TRUE/FALSE expressions) in the function to apply criteria to what's actually
added.

For instance, if we only wanted to add Col_B items where the corresponding
Col_A item is greater than 4...we could use this 2nd form of the function:
=SUMPRODUCT((A1:A3>4)*(B1:B3))

Each comparison of A1:A3 to 4 results in TRUE or FALSE.
Which Excel converts to 1 and 0, respectively, when multiplying.

So the source ranges become:
0 7 =0
1 8 =8
1 9 =9

And the SUMPRODUCT is: 17....(0x7+1x8+1x9)

For more information about SUMPRODUCT than you'd ever want to know
...see this link:
http://www.xldynamic.com/source/xld.SUMPRODUCT.html

I hope that helps.