A feature added into games upon the release of the Xbox 360. It was intended to be a bit of fun, but because Xbox Live is just the huge cuntfest that it is, it is now a number used to criticise other people.
If for example, someone has a low gamerscore they suck and should immediately give up on living. However, if someone has a high gamerscore then they have no life. These are not the only two parts of the spectrum though, because your gamerscore is the perfect balance of skill while still having a life.
I have a gamerscore of 77,770. Therefore everyone with 77,769 gamerscore or less sucks at playing video games. Anyone,with 77,771 gamerscore or more has no life.