Its nutritional output, compared to the effort put in, is pretty good. Potatoes are satiating, contain fairly large amounts of Vitamin C compared to other staples, and grow readily in conditions unfavourable to other staple crops. Ireland is a famously fertile island, but the frequent rains lead to damp soil, and, especially in the west, it is acidic, rough, and surprisingly unfertile. This meant that grain staples (wheat, oats, barley, and another New World import, maize) were not as popular for Irish farmers as they were in Britain, since the production process was more labour intensive and less profitable. Irish farmers instead preferred to use their land for pasture, and Ireland developed a dairy industry and livestock export market.
Thanks to the combination of these factors, the potato was an obvious staple. When mixed with butter or milk, it isn't missing any major vitamins. Comparable regions elsewhere in Europe, particularly Italy, saw frequent outbreaks of pellagra, caused by the low levels of niacin in maize, their staple crop. It was much easier to grow, especially in poor soil; it was much more efficient, and could be grown on comparatively small plots of land.
Throughout the eighteenth century, and into the nineteenth, this last point became increasingly important. The custom for inheriting land in Ireland had been to divide it equally among the male children, rather than simply pass it to the oldest son (I'm simplifying somewhat for brevity). The Popery Act (1703) codified this into law for Catholics, with the exception that, if the eldest son converted to Anglicanism, they would inherit the entire estate. The idea was to entice converts and reduce the number of Catholics holding large estates, but as the century progressed and Ireland's population boomed, those who refused to convert (and they were many) saw their holdings become increasingly small. For context, Ireland's population in 1821 was nearly 7 million - about the same as it is today. Great Britain's population was 14 million - today it's 66 million!
In England, this population boom had been absorbed by the industrial revolution, as rural workers flocked to factory towns and cities. Ireland, however, remained predominantly rural - even Belfast did not really develop as an industrial city until the latter part of the nineteenth century.
Most noticably in the west, there was now a large population, with smaller and smaller plots of poor quality arable land, far from industry or the chance to emigrate. The potato - easy, efficient, was the obvious choice for a staple crop.
This answer from 2017 by /u/Malicious_Latvians and the follow-up by /u/gothwalk covers the dependency part quite well.
Unfortunately I have no own expertise to help you further.