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Well, since any "parity" is really based off of edges, there's no real way to fix it while changing corners. It would be pretty hard to swap corners only, unless you can find an edge fix that fits well with a PLL we already know.
It stands for "Simple General Notation", Lucas made the acronym (and a program that displays algs written in SiGN) but I've been advocating it for at least a year.
The way it works is, outer layers and single slices are represented by capital letters, with a number before it to show which slice (so 1R would be the outermost layer of R and 2R would be the second slice on the R side), and block moves are represented by lowercase letters (so 2r would be a Rr move in old notation and 3r would be Rrl'). As a shorthand we omit the number for outer layer moves and double-layer block turns (so we write R instead of 1R and r instead of 2r). There are also ways to write more complicated block turns (such as 2-3r, r*, 4m) but most people won't use them so I won't bother explaining.