That red light on the individual plug is an indication of 'local breaker' tripping.
There is one for each pair of plugs and as you experienced it trips both seats. The most likely cause could be a higher power demand beyond what the plug was supposed to provide. If I recall correctly from a discussion on FT few years ago, the combined limit for pair of seats is ~150 watts and so if only 1 laptop is plugged then it is possible to get >85 watts in one outlet but as soon as something is plugged into the other and power demand exceeds limit, CB will trip and both plugs will glow red.

One thing which usually works in this case is disconnect from plug, give it 2-3 mins to reset internally (might still be red) and then plug back while disconnected at the other end - make sure you are not drawing power at the other end. After few seconds - if you are lucky - the light will turn green. If it doesn't then only maintenance guys can fix it.

As flyerCO pointed out there is no 're settable' CB for individual seat power and the pilot only has a master switch to turn IFE and seat power on/off for the entire plane.