Good question! I've been working in the .NET world for a good three years now, but I still find it quite challenging to come up with an acurate definition.
The way I see it, there is really two ways of defining .NET. First of all, there is an actual physical software component including a development framework and an execution engine (to be even more specific: mscorlib.dll and mscoree.dll).
Secondly, there is .NET used in the abstract. Microsoft is trying to market .NET as much more than a development framework and defines it in the following way on their website:
".NET is the Microsoft Web services strategy to connect information, people, systems, and devices through software."
In other words, .NET communicates the notion of connectedness and the ease of integration driven by .NET and the support of XML Web services.