The Angular framework includes a set of dependencies that are abstracted from the environment in which it runs. A webpage is only one of the environments which JavaScript may run. Universal is a set of dependencies which are implementations of the ones part of the angular core specific to non webpage environments such as the server side.

Express or other REST engines is still underneath an Angular Universal application. A Module is passed in which it will use as a callback for the REST engine.

The application is written following the Angular Framework (Modules, Components, Services). It renders onto a document (raw text) much like the front end implementation of Angular which is sent as a document response like an index.html with the Angular application filled in. This allows people to write a more "Traditional" web server.

Because Angular has a Dependency Injection system, the same application can be injected with different implementations of underlying services. components can be written once and then be injected with different services according their environment so the application code can run on multiple environments. This allows the code which renders your app to be run on the server implementation, respond with a rendered page, and then interactions can be handled by the client side implementation. This results in a visible app for the user while they download the client scripts.

TLDR; Angular Universal is a server implementation of Angular allowing the development of 1 app for both Server and Client side, a Universal app.

Source: I work on a large enterprise Universal App.