A type of early 60s rock 'n' roll which actually encompasses two distinct genres:
'Real' surf music - what purists call surf music is an instrumental, guitar-based form exemplified by Dick Dale, the Surfaris, to a lesser extent the Ventures, etc. This is drum heavy, with the melody played on the bass strings on the guitar, and is designed to simulate the experience of surfing. Usually has a slightly oriental feel to the scales used.
What most people refer to as surf music though is a pop music style which is influenced heavily by Chuck Berry and has an emphasis on vocal harmony - bands like the Beach Boys and Jan and Dean. The dividing line is not 100% rigid however, as the Beach Boys for example covered several Dick Dale tracks. This style of music is musically identical to the 'hot-rod' music also performed by those artists, as well as Gary Usher, Bruce And Terry, Ronnie And The Daytonas and others.