Putting an accused person to death, usually by hanging without a lawful trial.
While vigilante justice is nothing new - after all, it was the only kind before courts, police and superheroes were invented - the term Lynching is fairly recent. Most people associate lynching with the crimes carried out against black people in the 20's and 30's but it used to apply to much broader, and a little less horrible, practice.
It all started around 1780 when citizens of Pittsylvania County, Virginia got sick of all the criminals running around. They were far away from the courts and any semblance of civil authority. In steps Captain William Lynch who drafts a series of laws now known as Lynch Law. The gist: if we think you're a robber, we're going to inflict justice ourselves. Simple as that.
Interestingly, Ol' Willy wasn't a fan of the noose and instead preferred the punishment for caught criminals to be 39 lashings. Only later did hanging become part of the greater lynching family. Personally, I'd prefer to be tried by a jury of my peers but I guess that's just me...