Repairing wall around a plug socket
This is a simple repair that should only take a bit of time. The repair shouldn't be rushed so that the result is a patch that is hard to detect. Here is what you should do:    CAUTION must be used when working near electric wires and devices. It would be wise to shut off the breaker at the panel before attempting this repair!  Remove loose plaster sections (right side of receptacle) and brush out dust and debris.  Cover receptacle with masking tape.  Mix about 2 cups of plaster patch according to instructions and with a putty knife push into wall opening. NOTE: Work with the knowledge that the plaster patch will set in a few minutes. Stay focused and don't delay. Start along the outside edge of the opening pressing the patch enough to adhere to the wooden lathe and existing plaster.   You will need to apply a second layer for a smooth finish. Mix the same amount but add a teaspoon more of water. This will delay the hardening of the patch to allow some extra time to work the compound smooth. Have a 4 inch putty knife ready after the second batch is applied so that you will only need a couple of passes with the 4 inch putty knife to smooth the patch.  When completed the still wet plaster will appear slightly darker than the existing plaster wall, but when it is fully cured will become a brighter white which can be painted if needed. It should match the surrounding wall in texture and thickness.