Hm, right.
Basic problem: Writing tiles to the screen is slow. However, since few tiles usually change between frames, we don't actually have to write all of them. However, due to double (and more)-buffering, that can cause flickering. So we have a couple ways to deal with this.
2D: Use 2D graphics (SDL) for everything. This works everywhere; SDL deals with any double-buffering that needs to be dealt with. Kinda slow, though. Otherwise works basically like partial:0.
STANDARD: Actually, rendering the entire screen every frame isn't that slow, if you do it via OpenGL and have reasonable code. That's what this mode does.
PARTIAL: On some setups, just rendering the tiles that changed worked. Partial does just that; PARTIAL:2 renders each changed tile three times, in consecutive frames, to cover triple-buffering. Unfortunately many newer GPUs discard and overwrite the frame-buffer between frames, and then this doesn't work.
ACCUM_BUFFER: Uses the ancient glAccum call to save and restore the contents of the window between frames, working around the driver's discarding its contents. Usually the slowest mode of all, but some people have had good results. Presumably the others are even slower for them.
FRAME_BUFFER: Basically the same thing, but using newer GL frame-buffer extensions to render to a texture instead, and blitting that texture to screen once a frame. It saves at least one copy vs. accum-buffer.
Both frame-buffer and accum-buffer use partial:0 under the covers, they just wrap that method appropriately in order to avoid flickering.
VBO: A variant of STANDARD that uses vertex buffer objects to explicitly tell the GPU what data doesn't change between frames, namely the location of the various tiles. This marginally improves performance vs. standard, if it works, which it should.
SHADER: Dumps the entire DF graphics array to GPU memory, and programs the GPU to interpret it on its own. Dramatically improves performance, but basically only works on geforce 8000-series and above, or the equivalent ATI. I think there's some 7000-series card (7950?) that also supports such shaders, though. Doesn't work yet.