$eval and $parse don’t evaluate JavaScript; they evaluate AngularJS expressions. The linked documentation explains the differences between expressions and JavaScript.
Q: What exactly is $eval doing? Why does it need its own mini parsing language?
From the docs:
Expressions are JavaScript-like code snippets that are usually placed in bindings such as {{ expression }}. Expressions are processed by $parse service.
It’s a JavaScript-like mini-language that limits what you can run (e.g. no control flow statements, excepting the ternary operator) as well as adds some AngularJS goodness (e.g. filters).
Q: Why isn’t plain old javascript “eval” being used?
Because it’s not actually evaluating JavaScript. As the docs say:
If … you do want to run arbitrary JavaScript code, you should make it a controller method and call the method. If you want to eval() an angular expression from JavaScript, use the $eval() method.
The docs linked to above have a lot more information.