The Mutex class provides very useful functionality when you use multiple threads and you need to synchronize the access to a given ressource.
Imagine the situation when you have multiple threads which try to write in a file on the same time - if you don't synchronize the access an exception will be thrown.

You can do such a synchronization by simply using a Mutex.

public static Mutex WriteFileMutex=new Mutex();
...
mut.WaitOne();
...
code to write in the file should be placed here
..
mut.ReleaseMutex();