What is the most important use of AppDomains in C#?
The single most important use is that your code has to have one - i.e. everything you write in C# executes in an AppDomain. That is quite important ;-p
If you mean additional app-domains:
When using plugins and other untrusted code, it allows you both isolation, and the ability to unload them (you can't unload assemblies - only entire app-domains).
I'm using it currently to load dynamically generated dlls, so that I can unload them.
They also allow you to set different configuration files, trust levels, etc - but have associated costs of complexity and remoting.
MSDN has a section on app-domains, here.