I'd like to encourage anyone reading this who wants to correct or clarify anything I've said to feel free to do so. I'm answering based on my current understanding of .net, which will continue to improve as time goes by.
What is Visual Studio .NET used for?
Let's talk about .net in general first. .net is an underlying framework of functionality that is included with Windows XP and future versions of Windows. It will make certain types of programming easier, since some functionality is already built into the .net framework and won't have to be programmed. .net can be thought of as part of the operating system and is included with Windows, although parts of it are more like a separate layer linked to Windows.
.net is very similar to the Java Virtual Machine (JVM), which provides a framework of functionality so that Java applications can be smaller and thus more easily downloaded. Java programs can be smaller because they rely on functions in the JVM, which must already be installed on the user's machine. If the JVM (or .net) is not installed, of course, the program will not work, because the underlying framework of functionality is not there.
In Visual Studio, .net may be installed so that programmers can create applications that will run under the .net framework in Windows XP (or other future versions of Windows).
Is this used in conjunction with Visual C++ as a development environment?
Microsoft has, in effect, developed special languages that can be used to program in the .net environment. These are C# (C sharp) and VB.net (Visual Basic dot net). These languages include built-in links to the new .net framework.
Visual C++ will still be around and widely used, but it is not linked closely to the .net framework and so works outside of it (as it does now). Microsoft allows C++ code to be called from the .net framework, but as external functionality (they call it "unmanaged code"

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I hope my brief description has helped to answer your questions. I am currently a Visual C++ developer and have no immediate need (or desire) to program for .net.