What is "Ubuntu Web Browser"?

Even though Firefox is the default browser on the desktop version of Ubuntu, there's another option included in System->Default Applications.

Enabling this option brings up "Ubuntu Web Browser" with no titlebar menu and only a number of options in a small menu.

However, there's no information about what this browser is, what web engine it's based on, or even who built it (obviously we can presume it's Canonical, but then, why not say that somewhere?). There's no "About" in the menu, either.

The process appears to be called webbrowser-app. Calling webbbrowser-app --help yields some command-line options, but still no actual information.

$ webbrowser-app --help
Usage: webbrowser-app [-h|--help] [--fullscreen] [--maximized] [--inspector] [--app-id=APP_ID] [--new-session] [URL]
Options:
  -h, --help         display this help message and exit
  --fullscreen       display full screen
  --maximized        opens the application maximized
  --inspector[=PORT] run a remote inspector on a specified port or 9221 as the default port
  --app-id=APP_ID    run the application with a specific APP_ID
  --new-session      do not restore open tabs from the last session

And there's no man page either:

$ man webbrowser-app
No manual entry for webbrowser-app
See 'man 7 undocumented' for help when manual pages are not available.

Where is the information on this software?

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.

The browser is called Oxide (blog post announcing it).

How can Canonical be so remiss in providing no manpage, no "About", and no general information on how or what this software actually is?

File a bug.

I'll answer only on your first question:

Where is the information on this software?

I've been able to find the information about this software easily, using the native "Ubuntu Software" app: I found this "Browser" in the list of installed apps. It's said there:

Browser

Browse the World Wide Web

A lightweight web browser tailored for Ubuntu, based on the Oxide browser engine and using the Ubuntu UI components.

This is not much info, but this is all that was there.

BTW, by googling its description I immediately found an article mentioning it on Ubuntu Help Wiki pages and its project on Canonical's Launchpad (and the Oxide project too).