Acronym for Pick Up Group, in it's clearest definition a PuG is a group that is formed on the fly, made of people that do not know each other and attempt to accomplish a task (usually an Instance).
The term can also be used as a word, meaning to do something with a PuG (i.e. My guild wouldn't help me finish Mechanar, so I had to pug it). It can also be used to as an adjective, to describe a person that has been picked up on the fly for a group, (i.e. The pug Warrior is doing pretty good!).
As general rule, PuGs often have bad reputation and PuGing is often avoided or seen as a measure of last resort, since you have no way of knowing before hand about the skill, gear and integrity of your fellow party members.