If you're new to Irish music, it may seem strange to you that most traditional players learn tunes by ear, let alone that there are lots of excellent players out there who don't know how to read music. The very idea of doing without the dots and lines is enough to throw some people, especially classical players, into a panic. It somehow violates their conception of what learning music should be like, that you see the symbols and reproduce them and that's that.

But there's a lot more to Irish music than that. Nailing the exact notes with surgical precision is all well and good, but what matters a lot more are the things that can't be written down.
Learning by ear helps you to understand the large-scale structure of your tunes, which allows you to play around with the details. You can also learn tunes faster by ear and remember them more clearly, since you aren't putting the music through the filter of written notation. Learning from sheet music is like finding your way around a house by looking at a floor plan. Useful in its own way, of course, but when you learn by ear, you're wandering from room to room inside the tune, opening doors and peering into closets, finding your way around it.

Your experience of the music is more direct and intimate.