.NET is the most significant technology for developers around right now. It provides an environment within which a programmer can develop almost any application to run on Windows (and other operating systems).
.NET is a framework — an API — for programming on the Windows platform. It is used to write a dynamic web site, a server to server application, a XML Web service, a WPF application, a component of a distributed application, a Windows Service, a Control Panel applet, a database access component, or a Classic Windows application.
The NET in .NET is there to emphasize Microsoft's belief that a distributed application, in which the processing is distributed between client and server, is the way forward.
.NET introduced cross-language interoperability also known as mixed-language programming. Cross-language interoperability allows creating large, distributed software systems.
Since Windows 3.1, the Windows API has added many features and functions but has always kept backward compatibility. This has been crucial in the success of Windows. What began as OLE (Object Linking and Embedding), became COM (Component Object Model), then DCOM (Distributed Component Object Model) which became COM+. Throughout this evolution, applications written with one of these techonologies continued to work as they were upgraded.
With .NET, backward compatibility has not been lost. A .NET application written in version 1.0 will run on a machine with version 4 installed, for example.
With .NET Core, Microsoft has redesigned the .NET framework to be leaner, more modular and to run on MacOS, Linux and Windows. The .NET Core framework executables are distributed with the application.
Read about ASP.NET Core.