According to Eusebius of Caesarea, Papias was the bishop of Hierapolis and "a man of very limited intelligence" who lived sometime in the early second century. Limited of intelligence he may have been, but Papias is a very important source for the understanding of the propagation of the Gospels. It seems that he was in contact with people who knew Jesus' original disciples, as he writes in the introduction to his book The Sayings of the Lord Interpreted:
And whenever anyone came who had been a follower of the elders, I asked about their words: what Andrew or Peter had said, or Philip or Thomas or James or John or Matthew or any other of the Lord's disciples, and what Aristion and the presbyter John were still saying. For I did not think that information from books would help me as much as the word of a living, surviving voice.
It is interesting to note that Papias considers books less valuable as sources about Jesus' life than conversations, even though those conversations are what we would now call "hearsay" and FOAF information. It seems from this passage that most of the original circle of disciples -- Andrew, Peter, and so on -- were dead by the time Papias was writing, though his use of the present tense in the last part of his comment suggests that there were at least two eyewitnesses who were still living.
In the fourth century, Eusebius noticed Papias' repetition of the name John and tried to figure out what it meant. Since the second (i.e., the still-living) John was described by Papias as the "elder" (presbyteros in Greek), the standard assumption seems to be that this is the man who wrote the letters of John in the New Testament (the author of those letters calls himself "the elder" in two of his introductions). This leads Eusebius to the conclusion that the disciple John is not the same person who wrote the book of Revelation -- this latter is "the elder" in Eusebius' mind. Today, Biblical scholars generally agree that author of the Letters is actually neither of these Johns, and that none of them are John the Baptist either. But that's an issue for another node.
Papias is also our earliest source for the names of the authors of the Gospels (all four of the Gospels were originally written anonymously). Unfortunately, Papias' testimony has a lot of problems. He asserts, for instance, that the Gospel of Matthew was originally a compilation of Jesus' sayings written in the Hebrew language. However, modern scholars have made a very strong case for Markan Priority -- which means that Matthew's gospel was based on a document that was originally written in Greek. Lots of people have tried to find the "Hebrew" "sayings" of Matthew that Papias was talking about. Some have suggested that Papias may have had Q in mind, but this theory isn't very convincing either, since all the surviving evidence suggests that Q was originally written in Greek as well.
Papias says that the author of the gospel of Mark was Peter's "interpreter" (hermeneutes in Greek), and that he had written down "accurately, but not in order" everything that Peter remembered about Jesus. Papias' observations about Mark, which are preserved in Eusebius' Ecclesiastical History (3.39.15), seem to have something of a defensive tone: someone apparently was criticizing the gospel for its disordered and second-hand nature.
As with so many other important documents for the study of the Bible, Papias' book does not survive in its entirety. It exists only in quotations by Eusebius and a handful of other patristic authors.
Notes:
In this node I use Paul Maier's translation of Eusebius, published by Kregel in 1999.
Surviving references to Papias have been gathered, both in Greek and in English, on Stephen Carlson's excellent Synoptic Problem web site at http://www.mindspring.com/~scarlson/synopt/ext/papias.htm