Geoff is correct - the best way to understand Irish music is to immerse yourself in it.

In addition to Geoffs suggestions may I add: The Molloy/Brady/Peoples album whose name I don't have is a tour-de-force of the subtlety and rhythym of trad Irish. Also look for Planxty, Cran and the Chieftans (Water from the Well is particulary recommended).

A good bodhran player will be of assistance here too to really get in to the rhythms, and I would say Colm Murphy's album 'An Bodhran' is a good place to start.

And wait until you start with the English ones!