It's well attested to that raiders and settlers from Scandinavia had a substantial impact on Irish society. In some instances we can still be point to this influence in contemporary Ireland.
First, a brief history of Viking contact with Ireland. The first recorded reference is from 795, when it was reported that they raided a monastery on Rathlin Island (just three years after the famous raid at Lindisfarne, England). At this time Irish craftwork was among the most prized in Europe, so plundering these largely undefended monastic settlements (centres of wealth in rural Ireland) must have been extremely rewarding for the raiders.
For the following few decades the Norsemen continued to perform hit-and-run raids on Ireland, until around 840, when it was reported that Viking raiders were wintering in Ireland. Around 900 the Norse warriors were beginning to settle permanently on the island. Throughout the 10th century their influence were constant features of the many Irish kingdoms’ warring, often acting as mercenaries for the Gaelic kings, if not in their own right. Their influence as political actors began to falter from around the end of the 9th century (famously at the Battle of Tara (980) and the Battle of Clontarf (1014)). Like what would happen to later Anglo-Norman settlers, the Norse settlers largely became Gaelicized, becoming integrated into Irish society, likely within just a few generations of settlement.
Although this is hotly contested in early medieval Irish historiography, the Vikings are largely credited with bringing urban settlement to Ireland. Likely some proto-urban settlement existed, known by historians as the “monastic town”, but by our own definition of town (or even that of a medieval German or French person) this argument does not hold water, and they were still largely agrarian. From the early 10th century the Vikings established settlements that remain to this today Ireland’s primary urban centres – Dublin, Wexford, Waterford, Cork, and Limerick all being set up by Norse settlers during this period.
Modern Irish is still littered with words and phrases that can clearly be recognised as coming from Norse. A few examples: Gaelic words for garden (gairdín), shoe (bróg), river (abhainn), boat (bád), and market (margad) all suggest Norse origin. This also provides another insight into what influence these settlers might have had on Irish society – likely concepts such as ‘a garden’ (as in an enclosed area) or ‘a market’ where not words which were needed by the Gaelic Irish before the Norse brought them.
Another linguistic insight into Norse influence on Irish society can be drawn from place-names. For many towns or settlements, the only evidence historians have for Norse influence is the name. For example, Leixlip, Co. Kildare is drawn from ‘lax hlaup’, Old Norse for ‘salmon leap’. A town such as Wicklow also likely has Viking influence, as the ‘wick’ comes from the same Norse word that the ‘vik’ in Viking does, referring to a bay or inlet. It’s the same root that English towns, such as Norwich, come from.
Although I know not so much about this, the archaeological evidence suggests a merging of Norse and Irish styles of craftwork.
The Vikings established a trading network that extends across an enormous portion of Eurasia, and even into Africa and North America. Viking trade set Ireland among this network and fixed the island into an international commercial world. One of the most incredible examples of this is an 8th century coin from Iraq being found during an excavation of a small Hiberno-Norse settlement in the south-east of Ireland.
This list is by no means exhaustive. If anyone has any questions I will certainly elaborate on the evidence for what I’ve said. Some historians I would recommend for you check out if you would like to find out more would be Howard Clarke, John Bradley, and Colman Etchingham.
https://www.ria.ie/towns-viking-origin This website should also provide some interesting information if you're interested in the urban aspect of Viking influence.