The adoption of family names (or surnames) in Europe started in the 11th Century and in the main, fall into one of four categories:

 - Occupational names which describe a profession. 
 - Locational names describing a dwelling or place of origin. 
 - Descriptive names which describe some physical characteristic or mannerism. 
 - Patronyms which are the adoption of the subject’s father’s first name as a surname.

The locational surname ‘Warburton’ is a corruption of the old English ‘Werburg’ and ‘tun’ denoting a 'person from Lady Werburg’s manor or estate’.  The village of ‘Warburton’ can be found in the North West of England, Latitude N53:24:11, Longitude W2:27:21 (WSG84) situated in the county of Cheshire, close to Manchester and Warrington.
Google Maps provides a map of the area.

Blazons-of-arms, or "Coats-of-arms" as they are more commonly known, originated as motifs carried on the shields of knights in order that they could be identified on the battlefield. Not every family has a Coat-of-Arms and sometimes only a particular branch of a family has a Coat-of-Arms.

A coat-of-arms was granted to a family member when they were given the right to bear that coat-of-arms.  These armorials were formalised and recorded as heralds from the 13th Century onwards with crests and mottos later supplementing the arms. 

Since many unrelated families share the same surname it does not necessarily mean that someone with the same surname automatically shares the right to use that armorial.  Also, families having different surnames can share the same coat-of-arms.

The Warburton blazon-of-arms, as recorded in Burkes General Armoury, consists of "Argent, a chevron  between three cormorant gules".  Argent : the colour white used in a coat-of-arms, is intended to represent the metal silver, or, figuratively, purity, innocence, beauty, or gentleness. Gules : The colour red, and indicated on a blazon by vertical lines. (source: Webster's revised unabridged dictionary).
The Warburton motto is “Je voil droyt avoyre