Mono is a cross-platform implementation of the pieces that make up the .Net framework, like the CLR, C#/VB.Net compilers, and the base class libraries. Currently, Mono supports just about everything available in .Net 2.0. There are a few notable exceptions, like Windows.Forms' DataGridView and ASP.Net's WebParts. There are also a couple of namespaces that don't really have a Linux equivalent like EnterpriseServices, System.Management, and System.Messaging.
The .NET Framework is Microsoft's platform for building applications that have visually stunning user experiences, seamless and secure communication, and the ability to model a range of business processes. And it is Only for Windows Platforms.