Oh man, this is complicated and depends on what you mean by "Ireland's role." Ireland was officially a neutral country during WW2 (much like switzerland), but given its proximity to Great Britain and its border with Northern Ireland it still inevitably ended up fairly entangled in WW2 politics.

So, obviously to preface this, why the neutral status? Well, Ireland got into a war for independence very shortly after WWI, which was followed almost immediately afterward by a brief civil war over the status of Northern Ireland. Relations between the newly christened Irish Free State and the UK were still really frosty by the mid 1930s. Adding to this, the U.K and Ireland were embroiled in a trade war for most of the early 30s, which devastated the Irish economy. So the Irish government wasn't exactly raring to help the British, but siding with Germany would likely make the new country very vulnerable to the U.K.

So they officially went neutral. However, in practice, while the neutral status officially meant no preference to either side, allied forces tended to benefit the most. Allied aircraft crews that crashed in Ireland were generally rescued by Irish officials and usually allowed to return unmolested. In spite of their recent history, Ireland would also frequently give the U.K headsups about uboats spotted in Irish waters and collaborated with British intelligence over German threats. The war continued on in the north (which remained with the U.K) and some areas, like Belfast, experienced heavy bombing because of the shipbuilding yards located there. The south was also bombed on accident by the Germans a few times, including one incident where a bombing in Dublin killed almost 40 people.

However, its neutral status didn't exactly prevent Irish citizens from fighting on either side. Several thousand Irish men, including Irish army servicemen, signed on with the british army and would go on to fight in a broad variety of theaters in the war, though they faced a great deal of social stigma on their return home (you can read more about this here, and I can probably dig up more resources about this later). Unsurprisingly, a handful of Irish citizens (mostly IRA involved) fought for Germany, too, though there weren't as many. A ton of Irish citizens also emigrated (some permanently) to the U.K to work.

Speaking of which, the IRA remained an important figure as well during The Emergency. Distinct from the pro-treaty Fianna Fail government lead by De Valera, the IRA worked largely underground and there's a lot of evidence to suggest that it collaborated with Nazi Germany in making a bunch of tentative plans for a German invasion of Great Britain from Irish staging points, though none of these plans really got anywhere (check out Mark Hull's book Irish Secrets for more info). The Irish government also devoted significant resources to cracking down on IRA activity during this time. There seemed to be some British anxiety over the possibility of an IRA assisted incursion, and they actually made a tentative offer to hand over northern Ireland to the free state, though de valera refused (since this would almost certainly have kicked off another civil war).