> OK so basically appeal to authority etc.

No, I'm not making an appeal to authority. Sorry if it sounded like that.

The team behind Zcash has serious technical chops, and it's worth pointing out that some of the most competent cryptographers and engineers in the world are working on this project.

They've openly published the paper behind their protocol and their code base is open source. They aren't going the "trust us, we're kind of a big deal" route.

If you want to understand, read the paper: http://zerocash-project.org/paper

...and the source code: https://github.com/Electric-Coin-Company/zcash

If you don't want to bother to understand (e.g. if you don't consider yourself a subset of "really smart people"), then you have to find some other metric to decide whether or not to trust it. I offered the backgrounds and reputations of the people involved as one possible heuristic, but feel free to choose another if you prefer.

Most people don't understand how the Internet works, yet they manage to use it every day. Same goes for existing mainstream financial systems.

Well the question really is, how do the masses start to use this? If only couple of smart people understand it, it won't help much. There are already lot of "like bitcoin, but anonymous" coins, which haven't gained that significant success. If most of the people can't understand why this one is "the shit", they aren't going to see difference between this and the other privacy-promoting altcoins.