The surviving Gospels were not written until circa 70 AD onwards, although they seem to have been based on earlier sources. So, for the period between Jesus' time and the creation of the first written sources about him, we are dependent on the vagaries of oral tradition and human memory.
Ehrman looks at the psychological evidence on the fallibility of memory. He shows how honest and mentally normal people can develop memories of events that are flawed or even quite false. Even vivid memories may be inaccurate. This is admittedly counter-intuitive - we tend to assume that a memory that seems real is real. But it isn't, necessarily. We do tend to remember the gist of things, but we can't be sure that we've remembered more than that.
Ehrman is not making an argument for total, blanket scepticism about the Gospel narratives. It is more subtle than that. There are "gist memories" of Jesus in the Gospels which were handed on by Jesus' disciples and then preserved by those to whom they told them. For example, Jesus was almost certainly executed by crucifixion on the orders of Pontius Pilate, the Roman governor of Judaea. But the details of how this came about differ in each Gospel. And the differences are not random or innocent: most notably, as time goes on, the Gospel accounts of Jesus' trial and condemnation become increasingly pro-Roman and anti-Jewish. It cannot be a coincidence, from this point of view, that tensions between Christians and Jews were growing in the period during which the Gospels were written.
This is an object lesson in how false memories are formed and spread. In reconstructing the historical Jesus, we're not just up against the frailties of individual memory. It is now believed that none of the authors of the books of the New Testament were eyewitnesses to Jesus' life. (It wouldn't have solved all the problems if they had been - it has been known for years in the legal and psychological worlds that eyewitness testimony is not particularly reliable.) They were dependent on the accounts of others, and the successive retellings of those accounts would have been shaped by the early Christian community's own evolving sets of concerns.
The process would have been quite anarchic. From his lifetime onwards, people would have gossipped about Jesus in all kinds of settings. Research shows that stories can spread very quickly even in circumstances where no-one has access to tools of mass communication. In the course of "serial reproduction" of this sort, material quite quickly gets omitted, changed and reinterpreted.
In this connection, Ehrman makes it clear that certain views often encountered in biblically conservative Christian circles are wrong. It is sometimes said that the existence of a group places constraints on how far received stories can go astray. But the evidence suggests that group memories may be less reliable than individual memories. It seems that group members tend to acquiesce in mistakes made by other members, particularly those who are dominant personalities. It is also false to assert that oral cultures preserve stories more accurately than literate ones - indeed, oral cultures have less of a concern with accuracy beyond the "gist". This has been known at least since Parry and Lord's researches into oral poetry in the 1930s, and it is illustrated further by the work of anthropologists such as Jan Vansina and Jack Goody.
Does it matter if Jesus really delivered the Sermon on the Mount the way it is described in Matthew 5-7? It matters to me historically. But if Jesus didn't deliver the sermon, would it be any less powerful? Not in the least. It is, and in my view deserves to be, one of the greatest accounts of ethical teachings in the history of the planet.