AngularJS and Handlebars - both required or not

You are right, Handlebars and Angular together would be pretty useless.

Handlebars and Angular are completely different things.

Handlebars is a template engine. You write a fancy templatey-string, give it a JSON object, and it renders out HTML from the data. There's no data-binding, no updating, it's just a once-off render.

AngularJS is an HTML compiler and databinder. Angular will look through the HTML for angular-templating tags, interpret/compile them, and update the HTML with changes to data on a given controller scope. Angular doesn't just render an HTML string once, it compiles the HTML, binds it to a scope, and updates when data on that scope changes.

Handlebars in one picture

AngularJS databinding/templating in one picture

AngularJS's HTML compiler in one article

AngularJS's whole overview/guide, so you can know how it actually works