As you may know, Canonical is working hard at making Ubuntu the first convergent-ready operating system available, the company’s main focus being Ubuntu Phone, Unity 8, Mir and Ubuntu Snappy Core (Ubuntu for IoT).
The main idea behind the convergence concept is to create an operating system that uses the same code and applications on both the desktop and the mobile platforms and this is difficult because some features specific to on platform (phone/desktop) would not be usable on the other platform (desktop/phone).
This is what Canocanil’s Zoltán Balogh wrote on developer.ubuntu.com:
“When we talk about convergence we mostly mean application convergence. The “definition of done” is when one can start an application on a touchscreen phone and the application scales and adapts automatically to a bigger screen with keyboard and mouse when plugged into the device,”
A convergent application is the Ubuntu Notes application, which can be seen at work, in the below video: