Transparency is when you make the background of an image or sprite clear. Or non-existant. This means that there will be NO background in the image. Transparency is important to most GIFs. It gives them a more professional look. Think about this: Animated GIFs don't look very good when they're inside of a colored block, do they? Here, I will explain to you how to take the backgrounds away from images and sprites, using a GIF animator.

First, get the sprite you plan to give a clear background. Here, I used a simple Goku sprite as an example.
Notice how the background is the same color, and that color is nowhere else on the sprite itself. This is how it should be. If the background color is somewhere else on the sprite, bits and pieces of the sprite will be missing when you make it transparent.      \/
Transparency
Now. Make sure that sprite is saved in a .GIF format, then open it into the GIF animator. Look for options somewhere on the animator that mentions transparency, then select it. (It'll most likely be a box that you check.) Then preview the sprite. If the sprite's background is NOT the bright green, or whatever color you've used, then that means you've successfully made it transparent. Now, notice that same Goku sprite has no background, after making it transparent. It looks like the background to it is simply white, but it actually has no background. If you were to save that sprite, and post it on a page with a different background color, it would look like the background color was the same as the one on the page.
Transparency works the same exact way with images. Though, you may have trouble taking the background away from image, if it has multiple colors. However, if you have a program like Adobe Photoshop 7, taking backgrounds away from images is simple.
If you have any questions concerning this tutorial, visit the forum. The link is at the top of this page in yellow.