summing mixers are basically a way to mix your tracks together in the analog domain, instead of the digital one. some people believe that mixing tracks digitally (specifically, the summing portion of adding them together into a stereo mix) results in poor results, as far as the “width” or “sound stage” of your mix; or some variation of those ideas… they also like the idea of being able to push given channels and lightly saturate them, etc.
so the idea is you route a bunch of stems of your mix (either individual tracks or multiple tracks sub-mixed) out of your DAW, into a summing mixer which then combines them, then out of the summing mixer back into the DAW to be recorded as a final mix. along the way, some will add a favorite EQ, pre-amp, etc to further color the sound.
that’s the basics of it, at least.