The prefix Mc : Brides to McBrides

My research in Meath took my Brides to McBrides.  I know that at one time I knew what that meant, but I have forgotten.  Can anyone tell me what the prefix Mc meant?  And when did it happen?  Was there a time period where everyone did it or was it only after a certain generation or was it just random or personal preference?

Thanks in advance for helping me understand the change.

Barbara