The 'O' in Irish surnames means 'grandson of'.
In ancient Ireland the population was much smaller than today and the mass movement of people was uncommon. It was usual therefore for a person to be known only by one name: Niall, Eoin, Art, etc. Once there was no one else in the locality with the same name then this was not a problem.
The Gaelic Clann system was well established and this gave people a common identity with their people of the tribe and with the commonly shared area. This single name system began to break down during the eleventh century as the population was growing and there was a need for a further means of identification. The solution was to adopt a prefix such as Mac (Mc is an abreviation) or Ó. Mac means 'son of' whilst Ó means 'grandson of'. Mac surnames are generally of a much later date than Ó. The vast majority of Gaelic Irish surnames were created during the eleventh and twelfth centuries.
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