This was a recent job i was called to investigate. Classic effect of a poor connection between a plug and socket, resulting in heat generation. The level of damage and the discolouration traveling up from the socket connection suggests it was becoming a fire risk.
This can occur with old sockets, where the spring clips that make the contact on the plug weaken over time. On this occasion however, the issue was down to the fact that panelling had been fitted to the wall.
The resulted in the socket being recessed in the wall which meant the plug could no longer be fully inserted into the socket. A poor connection resulted.
This was resolved by fitting a new back box to bring the socket forward, allowing plugs to be safely fitted one again.

Other situations that can cause this type of socket fault:
Where sockets are installed close to obstructions below them (sometimes occurs when installed on a skirting board), which prevent the plug being installed easily. This also causes hazardous damage to the cable entering the plug overtime.

Damaged plugs, eg with bent pins that are difficult to fit, can prematurely wear the spring clips resulting in the same damage, even when a good plug is installed.

Drop me a line if you have an concerns over the power sockets in your home, and we can arrange a time to inspect/review.