Bay leaves were considered holy and associated with Apollo by the Greeks. The winners of the famous Olympic games,  beginning in 776 in Olympia in honour of Zeus, were decorated with a wreath of bay twigs.

The change from olive to laurel was due to the influence of the Pythian Games, which were conducted in honour of Apollo in Delphi (Southern Greece), starting 582. 

Much later, the Roman Emperors made use of the laurel wreath as a symbol of the god Apollo.

The Roman poet Ovid tells the story of the Greek nymph Daphne. Her father, Peneus, changed her into a laurel tree so that she could avoid the amorous advances of the god Apollo. From then on, Apollo wore a wreath of laurel in memory of Daphne.

'Neither witch nor devil, thunder nor lightening, will hurt a man in the place where a bay tree is.' 
~ Culper 17th Century.