Why do people of Irish descent have blue eyes and black hair?

The original Irish came from what is now northern Spain after the last Ice Age. The Irish Y-DNA is very similar to that of the Basque people. The people of that region are usually dark-haired as many Irish are, light-skinned (when not tanned), and some have blue eyes as well as lighter shades of hair. The Irish seemed to have retained the dark hair but experienced a mutation in the eye color becoming lighter.

As far as the Viking contribution, a study by McEvoy et al detected little trace of Scandinavian ancestry in the Irish male population.

He suggests that Norse colonial settlements may have been largely composed of indigenous Irish. It more complex than Spain+Norway = Ireland.

Previous answer:

the Irish are a mixture of Meditteranean (Spanish in particular) and Scandanavian people (Vikings from Norway) which probably gives rise to the common Irish phenotype of dark hair, pale skin and blue eyes. This combination is not very common in many other countries, I am Irish and have this colouring. People comment on my appearance a lot when I travel and its only then when I realise how unusual it can look. Megan Fox, Patrick Dempsey, Pierce Brosnan, Lauren Graham, Ben Stiller and Mel Gibson are all people of Irish descent who exhibit this characteristic