If you have never come across references to Q in scriptural study it is a hypothetical and highly speculative construct. It is sometimes also referred to as the Q Document or Q Gospel. A number of scriptural scholars have asserted that to explain the similarities between the Mathew and Luke Gospels as well as the disparities between these two and Mark there must have been a source earlier than Mark. Think about that for just a minute.
If it makes sense then you might have a lucrative career in Christian apologetics. If Q is an earlier source to all three why focus on disparities with Mark alone. For that matter, why would the disparities be so obvious to begin with. These three are often labeled the Synoptic Gospels for the similarities that exist among all three. This too makes very little logical sense since the differences are as numerous as the similarities. They are only "synoptic" in comparison to the 4th Gospel, John. Lets face it, that one is just flat out crazy.
So where does Q come in and what is its usefulness? It comes in as an attempt to make sense of something that does not really need much explanation. Most scholars who have promoted the Q hypothesis will freely admit that the Gospels most likely started out as oral tradition. It is also virtually impossible to deny that there are potentially multiple written versions. I say "potential" since it is hard to verify. Nearly all of the books of the Bible (Old and New Testaments) only exist in fragments. Much of scriptural study amounts to cobbling together pieces that are most alike. If you are looking for similarities odds are good that you will find them. One aspect of Q that few scholars ever address is why they see a need for such a document to exist. It really does not make sense to insist it has to be so.
No one has ever found let alone verified any candidates for being part of this supposed lost gospel. Actively looking for Q seems like a tremendous waste of time and resources. If while seeking out and studying other sacred documents a candidate is found I would be the first to encourage renewed investigation. Finding Q would be an amazing discovery. Though, it would still not be the proof of Jesus existence that some seem to think it is. That, however, is another matter altogether. I would end by pointing out that this type of wild speculation seems to be limited to scriptural/theological study. Folklore has no problem coping with differences and similarities within narratives that do not seem to have one original source. Stories of dragons make a good example. There are tales of creatures around the world that are generally viewed as being about dragons. There is no one written source that all others are drawn from and I'm unaware of a single folklorist having a problem with that.
If anyone is interested in Scripture studies or the history of the early Christian Church (Judaism as well) I consider the follow books to be good introductory materials:
Karen Armstrong The Bible: A Biography
Tim Callahan Secret Origins of the Bible
Alan Dundes Holy Writ as Oral Lit
Bart Ehrman Lost Christianities
Stephen Harris Understanding the Bible
Ehrman actually has a new book that is due to be released March 20th that I am anxious to read.