Originally I believe GIF disposal 'background' meant to dispose of the last frame area to the background color which is stored in the GIF image.
However The web browsers never did this (starting with the first real browser 'mosaic'), but instead always disposed to 'transparency', or the page background coloror texture. As this gave GIF animations a practical and popular application, no animation program I know of actually maked proper use the 'background color' attribute of the GIF image file format, as it was intended.
In essence dispose background may as well now mean dispose to transparency, rather that dispose to background.
The background attribute is now generally ignored, though can effect some image processing options in IM (as IM will use it if the 'background' color setting has not been set when a GIF image is read in, and used).
For example
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convert image.gif -alpha remove show:
will show the background color form the GIF image.
For example, I did not set my GIF background color properly when I saved my 'IM examples splash logo', so it can some out horible...
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convert http://www.imagemagick.org/Usage/images/splash.gif -alpha remove splash_alpha_remove.gif
This is different to using the actual 'transparency color' used to define palette boolean transparency in the GIF, which you get if you just turn transparency off!
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convert http://www.imagemagick.org/Usage/images/splash.gif -alpha off splash_alpha_off.gif
Note that using 'dispose previous' also means the same thing if ALL the previous frames are also all dispose previous. The only time dispose previous actually means 'previous' (rather than transparency), is if you have a previous frame that has some other form of disposal. And that dispose undefined (which is a valid disposal setting), is generally thought of as the same as dispose 'none'
Disposals are all exampled in IM Examples, Animation Basics.
http://www.imagemagick.org/Usage/anim_basics/#dispose
How animations use disposals will determine the 'style' or 'type' of animation generated.
http://www.imagemagick.org/Usage/anim_basics/#types
Mixed disposals (other than perhaps the first frame) is rare.