Further info for the interested:

Circa 1169, the whole of Ireland came under English rule. The English did not treat the supposed uncivilized Irish natives very well. The Irish didn't like this very much.

As early as 12th century, there was small scale immigration to Ireland from England. In the 16th and 17th century, we had the plantations of Ireland, when the English began forcibly taking land from the Irish and giving it to coloners from England. This happened primarily in Ulster and Munster, leading to a larger population of English in the North of Ireland than the south.

The highland clearances (Scottish nobles fleeing from Scotland) added to this slightly in the 18th and 19th centuries, but to a much lesser extent.

Jump to late 19th century, Irish fought back with Irish Republican Army, in a bloody war.

1914 Home Rule begins - Irish have mostly control over their own affairs, but still swear allegiance to the King of England. Better, but the Irish still don't like this. Outbreak of WW1 stalls proceedings.

1916, Irish republicans (who want complete freedom from England) staged the "Easter Rising"; 7 days of Irish fighting English. English crushed this, but it reignited the idea of Irish using force/fighting to get rid of the English.

More fighting ensued.

1922, the English offered an ultimatum: Get independence from England for the majority of Ireland, but the small pocket of Unionists (who want to remain part of United Kingdom) in the North will remain part of UK. This was the Andlo-Irish treaty. IIRC, the English said "Sign this, or we will flood Ireland with troops, crush all your rebellions, and direct rule will be reinstated". The Irish signed the treaty, thinking that the small pocket in the north would be too small to be viable, and Ireland would be united soon enough.

The border was drawn up, and the English took more than expected - resulting in the 6 counties of Northern Ireland.

Some Irish said "we have come this far, if we keep fighting, the English will take it all back". Others said "We have got this much, lets not give up! Fight for united Ireland!" These two groups fought each other for a bit.

Soooooo.....

Today, there is the Republic of Ireland - independent from UK, and Northern Ireland - a completely separate country from Republic of Ireland; different government, currency, laws, police etc. NI still under british rule, uses british pounds, can get british passports.

From mid-70's until early 90's "the troubles" were at their height. Republicans in Northern Ireland fighting (bombs, shootings etc) the English/Unionists in Northern Ireland.

Religion wise - Ireland was traditionally catholic, England protestant. So today, the majority of Catholics in NI are republican, and majority of Protestants are unionist.

There are still a minority of people fighting this fight: 1 Nov 2012: Prison Officer shot by Dissident Republicans

Timeline of Dissident republican activity March 2009 - October 2012

THE IMAGE

Every year on 12th July, Unionists have a parade to celebrate the Battle of the Boyne a turning point in the catholic/protestant fight in Ireland. Traditionally, these parades pass through republican areas, and the republicans don't like this being rubbed in their faces. They get angry and take to the streets.

The arguement goes like this: R: "Dont walk through here! It offends us" U: "Its our traditional route. It offends us that you want us to change it" R: "Rabble rabble rabble!" U: "Rabble rabble rabble!"

Hope that's understandable!

EDIT Added the stuff about plantation of Ireland and Highland clearances.

TL;DR - History makes some Northern Ireland catholics/republicans dislike some NI protestants/unionists, so sometimes they fight.