An Irish Bang is to have sexual intercourse without the use of contraception, with the knowledge that there's is still a risk of pregnancy.
It's original name was the "Catholic bang" but it became known as the "Irish bang" due to the English stereotype of all Irish citizens being catholic so the word catholic became Irish.
It is usually used in a way that suggests someone is good looking, or worth having sexual intercourse with in the same way "I would do that" would be used, but in a more extreme way.
Ed: Corr, look at that babe over there!
Dave: Yes mate, I would irish bang that and take all the risks.
Ed: Dude, you're not even catholic?
Dave: yeah, that's how fit she is!