TLDR;
Angular helps you deal with the complexity inherent in rich user interfaces. As UI complexity increases, the traditional model of generating pages on the server gets much more complex. Angular lets you decompose your UI into manageable chunks, and allows you to separate the UI from the implementation. This makes server-side page generation a great deal easier, but Angular really comes into its own when you make the move to pure javascript-based applications. A good example of such an application is Trello.
The long story
Angular isn't really targeted at sites that you can comfortably implement by generating everything on the server, and sending it across. Furthermore, whilst that is a perfectly good approach that works for many sites and applications around the internet, it becomes increasingly complex (thus difficult) to keep that approach working as you try to increase the level of interactivity in your site.
Ultimately the way you solve this is by pushing your UI more and more into the Javascript side of the equation. Angular lets you break your UI up into components, giving you clear separation between the look-and-feel, and the how-it-works. You can then build fairly simple pages on the server, and the JS front end is used to create a rich UI that makes separate calls back to your server for the data they need.
There comes a point, though, where all you want to do is server a stub page that loads a completely javascript-based application. Probably the most well known example of the sort of use-case where Angular really shines is Trello (it uses Backbone, not Angular, but it is the same use-case). There is a site http://builtwith.angularjs.org/ which has more example sites that use Angular.
So the short answer? Angular makes it easier to create rich, highly interactive user interfaces by letting you decompose your UI into components, and ultimately go completely javascript.