It interactively shows you each change that would be added and lets you decide whether it should be staged or not. Down to the hunk level, so you can partially stage a file if you so choose.
Oh, that's neat.
The -p presumably stands for pInteractive with a silent p :)
LOL it might stand for "prompt before"
Ha! It’s actually patch (as in select parts of the patch) though I remember it as partial.
There's -i for interactive, lets you add, patch and reset (unstage).