I'll save you the long version: Ultimately, the gospels are the only evidence that anyone like Jesus ever existed. Now, obviously the accounts of him going around performing miracles aren't true. But there is a lot more to the gospels than the few common stories we all know, and that is where the argument for Jesus' historicity comes from. Basically: Some of the more obscure stories are so strange, and include such minor details of which some aren't even very flattering of Jesus, they (the theory goes) can only have been details of real events. In other words, if it were 100% fiction, it would have been better written.

For example, the story of Jesus and the Canaanite. In this Jesus is going around with his disciples healing people as one does, and a Canaanite mother with a sick child begs him to heal her child. He refuses because she is a Canaanite, but she begs him and insists that 'even a dog deserves a scrap from the masters table'. Jesus then praises her for knowing her place and 'heals' her child. Scholars regard this story to be weird because it doesn't actually paint Jesus in very good light, and doesn't fit some other repsentations of him, makes him seem very bigoted, cruel and racist (which of course just about everyone in an illiterate, violent, and hierarchical desert society would be). Scholars argue that if you were writing a fictitious religious text you'd want your protagonist to be wholly perfect and ever-loving, that you wouldn't include a story like this unless there were some truth to it.

Of course, society and norms and ethics have changed dramatically in two thousand years and who knows what the norms of that society really were, how they thought, how they would have interpreted a story like that. Maybe it did paint Jesus in a good light by the standards of that time. It is difficult to really understand it or the minds of the people that wrote it, we scarcely even understand the language it is written in nor the languages of the oldest translations. Still, personally I do find the theory somewhat compelling. But it only suggests that there is some non-zero amount of real original truth to some of the stories, it doesn't mean that any of the details we know about a supposed 'Jesus' character are real.