What is "Ubuntu Web Browser"?

This is the browser designed for Ubuntu Touch.

It's designed for touch screen devices, and is not very intuitive when used with a keyboard or mouse. It's designed to be swiped with your finger.

This browser is a lightweight UI on top of the Oxide browser engine. The Oxide browser engine is just a web view control allowing a Chromium web view to be embedded in other apps. So, technically, it is webkit based.

It's only relatively recently that it's been included in the desktop editions of Ubuntu, and was never really intended to be used much on a traditional desktop, which may explain (but not excuse) the relative lack of documentation.