This unusual and interesting surname is Irish. Recorded in a wide variety of spellings including Trainer, Trener, Traynor, Trinor, Tronor, Trynor, Triner and Trinner, it may derive from the pre 10th century Gaelic Mac Threinfhir, meaning " the son of the champion". This name derives from the words "trean", meaning strong, and "fhear", a man. Traditionally Irish family names are taken from the heads of tribes, or from some illustrious warrior, as in this case.

A surname, also known as a last name or family name, is a fixed name shared in common with the members of a family and is passed down from generation to generation.  The use of a surname is relatively new in history and was adopted in order to legally distinguish two individuals with the same first name.  At first, these last names were not passed down to the next generation.

The Chinese were among the very first cultures to adopt the use of hereditary surnames about 5000 years ago. In Europe, surnames weren't used until the 10th or 11th centuries AD in Venice. Gradually throughout Europe, all nobility and gentry adopted surnames until eventually surnames were used by all Europeans of all classes.  

http://www.surnamedb.com/

http://www.irishsurnames.com/heraldiccharges.htm