Answer: Not much.
This is a question that comes up quite a lot. It usually goes something like this: "My PS Color Settings say sRGB, but my images are coming out in Adobe RGB. WTF?"
(Actually, not many people say "WTF?" I just added that for emphasis.)
If you shoot Jpeg, the colour space of your photos is set in your camera. If you shoot Raw, the space is dictated by your raw processor. In either case, Photoshop will usually honour that profile, regardless of its own "default" setting.
So, what is Photoshop's "RGB Working Space" useful for then? Well, only two things, really. One is when you make a new blank RGB image, it will assume that space by default, unless you specify otherwise in the "New" dialog. The other is when you open an image without a profile of its own, Photoshop will give it the default profile for as long as it remains open (but it won't save it with that profile, unless you tell it to).
Neither of the above circumstances arise a whole lot. For most of us, most of the time, we need to concentrate on setting the colour space where it matters - in Raw.
In ACR, you can choose your space in the Workflow Options (at the bottom of the screen). In Lightroom it's an export option, I believe.
The part of the PS Color Settings dialog that really matters is the "Color Management Policies" section. Unless you have a very good reason to do otherwise, make sure those are all set to "Preserve Embedded Profiles".
You can find more information about Photoshop's Color Settings in my article here.