For example original asciimathml script outputs mathml and since only mozilla (FF) browsers can render natively mathml (without extra plugins) other browsers need a fallback script that renders the same code with some other type of maths - originally with images and now lately we have started to use also mathjax fallback...
Or Tex filter tries to use first local latex binaries and if they are not found or they are not executable tex filter tries to use mimetex files as a fallback.
Usually "fallback" is an alternative which can be used if something goes wrong with the main plan.