1. The virtual DOM. When I'm writing jQuery-based code, I have to write both a component template and code that updates the DOM in response to input; when I'm writing code for a virtual DOM, the component template is sufficient to update the DOM and I don't have to write that extra code, so there are fewer chances for bugs to creep in.
2. HTML-like syntax embedded in Javascript (JSX). I didn't like this at first until I configured Sublime Text to highlight embedded HTML correctly. Embedded HTML has pros and cons, but I think it's a net positive.
React projects also typically include new tech like ES2015, webpack, hot code reloading, and Redux with its time-traveling debugger. You can build your own stack that uses a virtual DOM library, embedded HTML, ES2015, and so on, but it's helpful to start with a common stack that many people understand. That's why React is interesting.