I'm new to Dolphin, and yes, I've searched for an answer to my question here in the forums but couldn't find anything. Anyways, I get what Internal Resolution is, but I just don't understand what Full Screen Display resolution does and how it relates to IR. I would also like to know what kind of anti-aliasing Dolphin uses, as I only see super sampling mentioned in other threads, but I thought it was MSAA. Also, what do detail levels mean for each "level" of AA (I've never seen that before).
Internal Resolution is the actual rendering resolution, while Fullscreen Resolution is what Dolphin sets the system-wide display resolution to when in fullscreen. Generally you just want to leave the latter on Automatic, since that doesn't have any performance impact (except on Retina MacBook Pros, somehow).
Dolphin can use multiple kinds of AA – MSAA, SSAA, and FXAA are all built-in, and others are available via SweetFX and other injector tools. The control you're looking at is for MSAA, and the "detail levels" are defined by your graphics drivers (and are totally incomprehensible even to the graphics devs). The D3D(11) backend actually only supports MSAA – SSAA is only available in OpenGL (and the now-removed D3D9 backend) and FXAA is only available in OpenGL as a post-processing shader in builds newer than 4.0.2.