Many of the punk bands were young teens under the drinking age so they were often not allowed into music venues because of the drinking age restrictions. To combat this, groups of young punks asked to be allowed in if they marked X’s on their hands to show that they shouldn’t be served. Thus, we see the X's between straight and edge on the album cover.
Straight-edge was a song written by Ian Mackaye of Minor Threat that questioned the use of drugs and alcohol and instead advocated being present and keeping life simple, without the use of chemical enhancements. Ian himself was never a fan of drinking and drugs and the evolution of straight edge began with his song "Milk and Coke" for his old band, the Sklinkees. Unfortunately, the words of Straight Edge were picked up by fundamentalists and sparked a movement of crusaders against drinking some of whom turned radical and violent. Despite this, the message against drugs and alcohol was a sharp distinction from the way the media perceived punks.
"Straight Edge is a song about how you want to live. Keep it simple and be present"