Palla,
I suggest you look at the agile manifesto
http://agilemanifesto.org/ and the principles behind them
http://agilemanifesto.org/principles.html. That may help you understand agile as a methodology. Agile testing is just testing in an agile way, or testing on an agile project. We use both definitions.
I have used agile when working on a legacy system, although it is a bit tricker since there is usually a lot of technical debt (poor coding, lack of unit tests, etc.). Michael Feathers has written a book on the subject. I haven't used agile on a mainframe but I don't see why it wouldn't work. There are several articles on the subject - just google mainframe and agile.
As Sreerupa mentioned, eXtreme Programming is just one type of agile methods. Scrum is another. DSDL yet another. There are a number of them, but XP and Scrum seem to be the most popular.
Co-author, with Lisa Crispin: Agile Testing: A Practical Guide for Testers and Agile Teams (Addison-Wesley, 2009) www.janetgregory.ca