Straightedge is a label given to someone who does not drink, smoke, do drugs. It is purely a label, and means the same as teetotaler.
Straighedge first became known from a song by a band called Minor Threat, although the lifestyle existed before this band brought it to the public eye through a song, 'Straight Edge'. An X is often the symbol that people use to represent straightedge. There are several variations, XXX, sXe, and so on.
The media has portrayed straightedge as a violent group of people. It is true that there are sXe kids who go aroun beating people up, just as there are vegans, vegetarians, Christians, athiest, racists, anti-racists, who do the same thing. They beat people up because the don't believe in the same thing as they do. But this is a very small minority that are involved in this violence.
The same thing has happened with skin heads. There are only a select few who are actually racist and violent, but it is these few that are given all the attention, and so most of the world only sees a skin head as being a neo-Nazi. There are infact, anti-racist skinheads, gay skinheads, and so on.
If you want to learn more about straight edge, you can either go to my sXe links, or search the web for other sites. There are many of them out there.