Dispose to Background
Note: The gif format defined two kinds of dispose-one to restore to background color, and the other to restore to background image. However, all browsers that handle animated gifs don't descriminate. Dispose always means dispose to background, whether that background is solid color or a background tile or image. That is why we speak only of Dispose being checked or not checked (yes or no)

NO DISPOSE (not checked):
This means that the previous frame is retained, not disposed of. If all frames are nontransparent and same size, you will not notice anything. But if your frames change coordinates. size, and/or have transparency, then the presence of the previous frames is apparent. In some cases you want the previous frames to be retained, when you want either a trail or a buildup to occur. An example of using a trail would be to write out a word in handwriting. Having the full area of the final handwritten word on each frame will create an enormous file. However if you create an animated gif that starts out defining the full area on the first frame and then each subsequent frame is a small segment of the handwriting, and if there is no dispose, you achieve the effect of handwriting with an animated gif filesize that is only a little larger than a single static gif picture of that area. I would use the Boundaries optimization, turning transparency on and dispose off. Another use is a buildup effect. Let's say you have a composite picture of many pictures and text. You can use an animated gif without dispose to build up that composite picture one element at a time.

DISPOSE (checked):
Dispose turned on needs little explanation because that is the normal situation for animations. It is the no-dispose situations (above) that offer new situations. The last frame is disposed of, so only the current frame is playing at any time. .

See also notes on dispose under 'Optimization'