I used PySide to develop for Qt on the Nokia N900. What a wonderful experience! The N900 itself is based off of debian. Deploying to the phone was as simple as scp. Running was as simple as sshing in and executing my Python script. It was really great to be able to run the same source on both my desktop and phone! I'm looking forward to using Qt on Android - even better if it is with Python!
I might actually do some proper Android development now Qt is there, mostly as I've spent that long developing with it I've got a lot of things in my tool bag. Nice work from all involved.
QT is a very popular cross-platform framework. Its mostly used in Linux and other POSIX operating systems (but it also available for Windows and other non-POSIX guys).
QT is not like phonegap in the sense that is both a high level and low level framework for creating apps for the Desktop and Mobile using C/C++. Other bindings exist so that you can use QT from other languages such as Python.
There is also QML which even though I have no experience whatsoever, I understand it to be a quick way to create an app using a declarative syntax not unlike a mixture of XML and a javascript-like language. I may be wrong on this one but I've heard that QML would appeal to Javascript fans.
Qt is a very powerful library for C++, probably most popular for writing GUI apps. Google Earth and VLC are written with Qt (using QWidgets).
QML is the new, declarative (finally!) way to define the GUI. Blackberry 10 is built atop QML 1.1 (Qt 4.8.4 with some custom improvements for QNX). QML2 in Qt5 runs the entire UI atop Open (E)GL 2 and is very responsive, even on some very old hardware. Last I read the equivalent to Android's 4.0->4.2 graphics backend overhaul isn't landing in master until 5.2, however :/
