Its source is Alice, an English name meaning "Exalted nature."
This originated as a surname, meaning in effect ''Alice's son.''
Generally, family names originated with a male ancestor, as the commonness of patronymics such as Johnson or Anderson attest. However, if a woman headed the household for any reason (such as, her ownership of the family property, the absence of a husband because of death or abandonment, etc.) notable exceptions evolved.
Another example of such a surname is Madison, derived from either Maud or Madeline.