Tell us more! I don't know anything about it either. Couldn't the UK have ceded it to Ireland? Or would the problems just have gone another direction?

There are two largely different concepts/epochs separated by more than 40 years.

The negotiations and partition of Ireland and the establishment of Northern Ireland as a self-governing province (rather than being governed from Britain):

https://en.wikipedia.org/wiki/Partition_of_Ireland

And then the Troubles, which were a sectarian conflict between Catholics and Protestants within Northern Ireland itself, that stemmed from Protestant oppression of Catholic rights protests (patterned after the US civil rights movement). The Wikipedia pages are really good, but the top level page is great because it covers the early days so well:

https://en.wikipedia.org/wiki/The_Troubles