Following Wikipedia:
The .NET Framework (pronounced dot net) is a software framework that runs primarily on Microsoft Windows.[
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So what is a Framework?
In computer programming, a software framework is an abstraction in which software providing generic functionality can be selectively changed by user code, thus providing application specific software. It is a collection of software libraries providing a defined application programming interface (API).[
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So it is a collection of software libraries?
In computer science, a library is a collection of resources used to develop software.[disputed – discuss] These may include pre-written code and subroutines, classes, values or type specifications.[
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So basically .NET is a rich platform used for software development, primarily on Windows.
So for example, when programming you will need to work with text and numbers (String and Integers), both are defined in the .NET Framework (if they weren't you might have to work with 1's and 0's... You don't want that).
You might have to create Services (in the ServiceModel library). Creating a service that may be accessed through http from any computer in a network is a near impossible task when having to do everything yourself. However, .NET does a lot of the work for you (and .NET itself is written in a framework that does a lot of work for the programmers of .NET). In this sense the hard part is abstracted away and only some implementation details are left to the programmer.
So what else does .NET handle for a programmer? For example memory management (which happens in the background, but which a programmer usually does not have to worry about when programming .NET), Exception handling (Exceptions are thrown up the stack until it finds a Catch block where it can be handled), reading or writing files (with System.IO namespace) and the list goes on and on.
You still have to make a lot of code sometimes, but calling a method File.Open("C:\MyTextFile.txt") is a lot easier than having to type something along the lines of "00110100101100100" (or whatever) ;)