I've read the Wikipedia page on functional integration, but it really isn't very easy to understand. There don't seem to be any online videos on the subject either. In addition, when I search online, I get results for the Feynman Path integral. It's a good reference, but it adds a lot of complexities to the problem of understanding functional integration. For instance, quantum mechanics is already hard enough, I can't really parse what's functional integration and what's QM formalism.
Could someone perhaps share some intuition/motivation for why the functional integral is defined the way it is? I'd really like to see a simple, but non-trivial, example worked out. I'm nearly clueless about how an infinite product of infinite bounded integrals converges, so a show-and-tell on how this works out in practice would be great.