Here are some piccus to illustrate it, sort of. Proudly made in Corel
http://www.prideofmind.com/images/demo.jpg
And a Corel version for you at:
http://www.prideofmind.com/images/demo.cpt
Pretty much, the different merge modes tell Corel Photo-Paint (or whatever other program you might use) how to draw things when there is one object in front of another. In multiply mode, it draws the object in front by multiplying its pixel values color-channel-wise by whatever's behind it. In my example there are 4 rectangles, and the one in the center is in front of them all.
The center one has an RGB color of 255, 128, 0 on the usual scale of 0 to 255. In other words, that's 100%, 50%, 0% for the purposes of multiplication.
So for example, when that square is in front of the pure green square (color 0, 255, 0), we get a blended color of (100% * 0, 50% * 255, 0% * 0) - i.e. (0, 128, 0) which is a darker green. The rest are left as an exercise to the reader.
As for the smiley faces, I put them there to show another example of multiply vs. regular merge.
Did that help at all? ^^;;;