There are two ways for a novice banjo player to listen to an Irish tune. The first is for enjoyment. We were all attracted to the lift and joy of Irish music and even though "it all sounds the same" to an outsider, there is plenty to enjoy and savor in the genre. For a beginning musician, however, there' that problem of learning the tune.
Because we are beginners, we are just barely out of the "it all sounds the same" stage of our life but because we have a desire to learn the music from the inside out, we do know that there is something essential about the music that we are trying to duplicate and eventually create.
One of the problems of listening to Irish music (other than not being able to listen to enough of it) is that people play tunes in a differently. They may play it slowly, with different emphasis on notes, with alternative notes or different timing. All of these factors change the way the tune is played and heard.
Most Irish tunes are simple in structure. While there are many exceptions, they usually follow a predictable form and with the exception of the the second half of each part are repetitive. There are very few "crooked" (i.e. extra beats) tunes in Irish music because it is dance music first an foremost. The dancers have to know what is going to happen and as a result, someone new to the music can also anticipate what will come next.
Part of this predictability is the notions of essential or basic notes in a tune. Every tune has notes that make it that specific tune. For the most part it is usually the strong notes, the ones that are also the emphasized notes in a tune. For a jig it can be notes one and four in a measure while the other notes are either passing notes or "interesting" but not vital. Reels are a little different as they probably have more essential notes per measure but they vary a lot more than jigs.
Here is a video of trying to demonstrate this principle. You will notice that I can't play and sing at the same time. My IQ drops 50 points when I try:
Once you learn the essential notes, you can go back to your favorite rendition of the tune and see how much of it is style and the player's interpretation. Knowing the essential notes also gives you a leg up when you read the notation. You can start picking out the tune from the notes and see where you can vary things without losing the essence of the tune.
As an aside, this is one of the reasons I recommend using notation to preserve the tune for further evaluation. TAB records the way a certain player does the tune and it is less obvious what the essential notes are. Memory sometimes develops new tunes but once you have a tune, you automatically parse out the essential notes.
So when you listen to tunes, think in terms of the skeleton. There are notes that support the whole tune and it is your job to eventually flesh it out. But first you have to have the basic form down before you can go on.