.NET Framework (pronounced dot net) is a software framework developed by Microsoft that runs primarily on Microsoft Windows. The prime attention seeking feature is a large class library known as Framework Class Library (FCL) and it facilitates language inter-operability, which means developers working on different module with different languages can easily integrate the application at the time of deployment and execution.
Generally, Microsoft .Net Framework is a platform that supplies tools and technologies required to build Networked Applications, Distributed Web Services or Web Applications.
What is ASP.NET:
ASP.NET is an intact part of Microsoft .Net platform and is used dedicatedly to produce interactive, data-driven web applications.