"What is involved in repairing this? Major electrical work?"

No, hardly any electrical work at all.

It's mechanical work, to securely attach the box to the wall (and move it to be flush with the wall). There may be screws or nails that have come loose; if they are inside the box then you will have to unscrew the outlets to get at those screws, then reattach the outlets to the box (this is probably the extent of electrical work, and even this won't require even detaching any wires). Otherwise the box may have a bracket extending up & down from the box itself, and that is where you would attach it to the wall.

The problem here is that what you need to get at is behind the plaster wall. Most of the work will be in busting out part of that wall to get access to it, and then repairing the plaster wall, sanding it smooth, and then repainting it. Drywall work, not electrical work.

You might try unscrewing the outlets and stretching them out on their wires, to see if it's possible to work from inside the box and run long screws into the nearby stud to secure the box in place. That would be the easiest.

Otherwise, get ready to do all the drywall & painting work as mentioned above.

Note that if the outlets themselves are secure, not moving around in the box when you plug & unplug cords (instead the whole thing moves as one unit), then this is not a seriously dangerous situation -- you don't have to fix this immediately. Just be careful when plugging or unplugging cords until you get it fixed.