Related links:
It uses Mozilla XULRunner as platform. As such, it is shipping with the Mozilla engine. TomTom made some small changes to Mozilla, mostly bugfixes and branding, which are published here.
The source code changes are available under the MPL, GPL and LGPL.
Note for clarification: The actual GUI source code (JavaScript, XUL, locales etc.) is not open source, neither is the "HomeServices" DLL (implemented as XPCOM module written in C++) used to access the device, neither is the HOME2 server. The source below contains only the Mozilla engine and changes to it.