Undervoltage in your mains (causing dim lights) could be caused by being a long distance from the local substation, or by inadequate wiring within your house (ie, cable diameter is too small). Lights can also dim when large motors are started (if you live near a factory etc).
Also, you can get a "brownout", when the local transformer blows a high voltage fuse, then 2 of the low voltage phases are at 50% of their normal voltage.
Regarding 2 and 3-pin sockets, the third pin (earth) has no function under normal conditions. What it does do, is provide a safe path for current to flow, if there is a fault in the appliance (eg, if an active/hot wire comes loose and touches the case). Without the earth, the case would become 'live', and anyone who touches the case risks being electrocuted. With the earth, the fuse would blow if this happened.