Irish/Scotch Ancesters

Mac, Mc. O' all in Gailic mean "Son of"
Ni means "Daughter of"

Names were also used as descriptions of the people that bore them:
McAllen, Allen meaning "handsome"
Brian O'Brian meaning "Brian Jr."

The very fiest recorded instance of an Irish person using a surname (they probably used them earlier, but this is the earliest recorded instance of it), was in 916 AD in Galway. The user of the surname was a Lord who called himself Tigherneach Ua Cleirigh. The "Ua" later became the modern O'. This Lord's descendants are the modern day O'Cleary families. When the Normans invaded Ireland in 1169, many Irish families using an O' Mc, or Mac surname changed it to the Latin Version of "sonof", which was Fitz, as this is what the Normans used. Other famillies kept their Gaelic surnames in spite of their oppression by the Normans.

Occupations became a factor in using surnames;
The ancient equivalent of giving someone their business
card. A baker, cooper, fisher, butler, thatcher, mason, smith, and wright all had ready surnames in their occupations

Surnames from a person or family's geographical location was another way:
A person who lived on ar near mountians or a hill may use "Hill" as a surname. The same goes with dales, or valleys, and rivers would use or incorporate those features into their surnames. Montgomery ("Mont", or mountain) and Mondale ("Dale")

In the 1500's when a new Protestant religion from England suppressed traditional Irish Catholicism, Protestants from England were given Irish lands and moved there, making the Irish second-class citizens in their own country. To adapt to their new circumstances, many Irish families Anglicized their surnames, allowing them to fit in with their new English neighbors. So names like O'Ceallaigh became Kelly, O'Murchadha became Murphy, and MacGabhann became Smith. The English who were their boss's and landlords were able to pronounce Anglicized surnames better than traditional Gaelic ones.

As you can see, learning the history of Irish surnames has helped me in my research into the Irish, Scotish, and English families who immigrated in the 1800's