I will try to explain the Irish border issue in simple terms.

The UK has a little brother Ireland.  For hundreds of years, the UK was in charge of Ireland (and in fact of a large part of the world, because they had conquered those countries with their powerful army).  About 100 years ago Ireland declared the independent Republic of Ireland (they had wanted independence much longer).  But in Northern Ireland, many people (a bit more than half) felt more British than Irish (because their great-grandparents had (been) moved from Britain, partly to suppress Irish independence) and this part did not become independent.  Ireland was, and remains, split.

Many Irish people were very unhappy with this, and there was a war.  To resolve this war, the UK and the Republic of Ireland agreed to have similar rules.  This way, people in all of Ireland could cross between the Republic and Northern Ireland without noticing the border.  Both the ones who wanted (nationalists, republicans) and who did not want independence (unionists, loyalists) were OK with that (at least OK enough to mostly stop fighting).  They could have very similar rules because they were together in the EU.

Now the UK will (most likely) leave the EU but the Republic of Ireland will not.  This means the rules will not be similar anymore, and the border between the two will become more visible.  Many people in Ireland, in particular in the part still part of the UK, are *very unhappy* about that.  They might cross the border twice a day or even have a farm that exists on both sides.  The EU and the republicans wants that Northern Ireland rules stay close to Republic of Ireland rules (so Northern Ireland stays a little in the EU), but the unionists (and many in the UK government) want that Northern Ireland rules stay close to British rules.  It is not possible to do both (unless all of UK stays close to EU rules, which is like staying a bit in the EU).  The current UK government needs the support from the unionists.

Therefore, for the Irish border question alone, it is impossible for the UK to leave the EU while keeping both nationalists and unionists happy.