Backbone is a clientside mv* javascript web framework. In fact it's really the oldest client side mv* javascript framework. The initial release for backbone was back in the ancient times of 2010. Backbone ushered in the new era of web applications with an mv* framework that sits in the browser and communicates to a server that is primarily in charge of data persistence.
Backbone is loosely based off of the Model/View/Controller pattern which was created by smalltalk developers and became massively popular for web development due primarily to the Ruby on Rails framework. Backbone and many other frameworks like it tend to have an explicit model and view and something of their own design that roughly approximates a controller.
The Backbone model provides the interaction with the data of a Backbone web application. It is the way that Backbone communicate with a server and provides both built in and programmer defined methods for manipulating data.
The backbone views define the way that a Backbone application displays the data gathered from the models. This is the way that Backbone interacts directly with the browser. The main difference between Backbone and other mv* client side javascript frameworks is that Backbone doesn't have built in interactions between the view and the model. All interactions have to be defined by the programmer.
The last major component in Backbone is the router. Backbone routers define what happens when a user navigates to a certain route. It really defines the interactivity of the application. It acts both as a traditional router and in many cases a controller. The backbone router will determine which models a route should grab data from and which views should be rendered to the screen.
Now you may be asking yourself "WTF would I want to learn Backbone when EmbAngular has all the magics?" Well, Ember/Angular have do make it very easy to create a single page web application but it does a lot of the interaction under the hood and learning one doesn't really give that much insight into the other. Backbone provides a great learning platform because it doesn't provide the programmer with a lot of magic. Once a developer learns Backbone it makes it very easy to learn another more complex framework.