The Collaborative International Dictionary of English v.0.48:

Patronymic \Pa`tro*nym"ic\ (-n[i^]m"[i^]k), a. [L. patronymicus,
   Gr. patrwnymiko`s; path`r father + 'o`noma name: cf. F.
   patronymique.]
   Derived from ancestors; as, a patronymic denomination.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Patronymic \Pa`tro*nym"ic\, n. [Gr. patrwnymiko`n.]
   A modification of the father's name borne by the son; a name
   derived from that of a parent or ancestor; as, Pelides, the
   son of Peleus; Johnson, the son of John; Macdonald, the son
   of Donald; Paulowitz, the son of Paul; also, the surname of a
   family; the family name. --M. A. Lower.
   [1913 Webster]

   Note: In Russia, the patronymic is taken routinely as a
         middle name, and is commonly used together with the
         given name in addressing people with whom one is
         familiar, thus Ivan Ivanovich would be commonly used to
         address Ivan, whose father was Ivan; likewise Boris
         Michaelovich would address Boris the son of Michael,
         and Lena Ivanova would address Lena, the daughter of
         Ivan.
         [PJC]

WordNet (r) 3.0 (2006):

patronymic
    adj 1: of or derived from a personal or family name
    n 1: a family name derived from name of your father or a
         paternal ancestor (especially with an affix (such as -son
         in English or O'- in Irish) added to the name of your
         father or a paternal ancestor) [syn: patronymic,
         patronym]