I am following a procedural stone texture tutorial and they showed this node group, this acts as the starting point for pretty much the whole texture, but I have no idea what it does. It basically takes texture coordinate object, separates xyz, and then subtracts data from object info
This is likely trying to add some randomness into the texture coordinates so all objects don't have a perfectly matching texture placement introducing some variation between them despite using the same texture.
It takes Object texture coordinates as base then separates each axis into separate components so an arbitrary value can be subtracted to in each direction (Color for X, Object Index for Y and Random for Z) and it doesn't always offset the same amount for each axis.
I do have some doubts about its real effectiveness, since as far as I know both Index and Color aren't really random, but is user adjustable values. On the other hand it does allow some degree of "manual placement" on per-object level.