This is a part of design of the BCL that kept me wondering for some time now. I find it kind of counter-intuitive, I fail to see the connection between Process and for instance the Debug and Trace classes.
The process class doesn't just represent a single process. It has a ton of information about the running processes on the computer. This info can be used to find problems or just get general information about your system state.
you can see the diagnostics namespace description here: http://msdn.microsoft.com/en-us/library/system.diagnostics.aspx
and the process class description here: http://msdn.microsoft.com/en-us/library/system.diagnostics.process.aspx