The synoptic Gospels are Matthew, Mark and Luke. And the word synoptic is a Greek word that means "seen together" and refers to the way in which the similarities between these Gospels allow them to be "seen" (-optic) together (syn-), because they tell so many of the same things about Jesus and often in very similar ways. The Gospel of John shares some things in common with these three but also a significant amount of additional material not found in the synoptics.
When we talk about the "Synoptic Problem," it is important to note that it is not really a problem or a difficulty in the sense that it makes it difficult to believe the Bible. The word problem is being used more in the same way that you would talk about a math problem. It is a puzzle to be solved. It brings up interesting questions that we would like to have answers for: Which Gospel came first? Did Matthew use Mark or did Mark use Matthew? Etc.... Below are some of the best resources available for understanding and exploring the issue:
*The Synoptic Problem Website by Stephen Carlson
*The Case Against Q by Mark Goodacre
*Jerusalem Perspective: "A Groundbreaking Attempt to Reconstruct the Conjectured Hebrew Life of Yeshua.....Under the direction of David Bivin, Jerusalem Perspective has launched an attempt to reconstruct the account of Jesus’ life which, according to church tradition, was written in Hebrew by Jesus’ disciple Matthew. Although this ancient eyewitness account is no longer extant, we believe that significant portions of this source have been preserved in the canonical Gospels of Matthew, Mark and Luke. If this theory is correct, then the first three canonical Gospels are the grandchildren or great-grandchildren of that conjectured Hebrew biography, which we refer to as the Hebrew Life of Yeshua. An attempt also has been made to reconstruct the first Greek translation of the Hebrew Life of Yeshua, a more immediate ancestor of Matthew, Mark and Luke."
*Lecture #6: "Form and Source Criticism" of Michael Kruger's FREE! Gospels course. You can also access it at Reformed Theological Seminary's iTune page or by using their Android app available at Google Play.
*The first 3 lectures of Robert Stein's FREE! online course "New Testament Survey -- Gospels" (35-40 minutes each)
*Last Seminary hosts five articles on "Q & the Synoptic Problem" that can be download for FREE--with brief abstracts for each.
*"On Dispensing With Q" by John Kloppenborg. A response to Mark Goodacre's book The Case Against Q.
*Redating Matthew, Mark & Luke: A Fresh Assault on the Synoptic Problem by John Wenham
*Is There a Synoptic Problem?: Rethinking the Literary Dependence of the First Three Gospels by Eta Linnemann. (Linneman was a leading liberal critic who told her readers to throw away all of her books when she got saved!)
*Three Views on the Origins of the Synoptic Gospels edited by Robert L. Thomas (contributors: Grant R. Osborne, Matthew C. Williams, John H. Niemela, and F. David Farnell)
*The Synoptic Problem: Four Views edited by Stanley Porter and Bryan Dyer (conributors: Craig Evans, Mark Goodacre, David Peabody, Rainer Riesner)
*The Synoptic Problem: A Way through the Maze by Mark Goodacre. Website for the book. Download the book for FREE!
*The Synoptic Problem and Statistics by Andris Abakuks
*Horae Synopticae: Contributions to the Study of the Synoptic Problem (1909) by John C. Hawkins is FREE!
*The Case Against Q by Mark Goodacre
An excellent Annotated Bibliography can be found at Stephen Carlson's website....
Also check out the lists of Websites, Books and Articles, Q Web Materials, and Reviews at The New Testament Gateway: Part of a large directory of academic internet resources, though sadly lacking in some of the best evangelical scholarship.