Strictly, triskaidekaphobia refers only to fear of the number 13, which some regard as a marker of bad luck, an ancient superstition that some writers credit to the Last Supper, after which Jesus was betrayed by one of the 13 present (some hosts will still take great care not to seat 13 around a table); others put the idea much further back, into Hindu mythology.
People who build hotels and office buildings know all about triskaidekaphobia, even if they do not know its name, since one almost never encounters an elevator that goes to the thirteenth floor!
Brave New Brain, by Nancy C Andreasen, 2001.
The term is often extended to mean fear of the inauspicious date Friday 13th, a double dose of unluckiness, as in some cultures Fridays have also been regarded as a day of bad luck because Christ was crucified on that day. It was once thought so especially by mariners, for whom it was long considered unlucky to set sail on a Friday. Some wag invented friggatriskaidekaphobia specifically for fear of Friday 13th, where the first element derives from the name of the ancient Scandinavian goddess Frigga, after whom Friday is named. The year 2009 has been a bad one for friggatriskaidekaphobics, since it was one of the comparatively rare ones in which that date turns up three times. Every year has at least one Friday 13th, but in each of the 28-year cycles of our calendar there are four years that have three of them; the years 2012 and 2015 will also have three such Fridays.
The word’s origins are all Greek, from tris, three, kai, and, deka, ten (so making thirteen), plus phobia, fear or flight.
The word is a comparatively modern formation, dating only from 1908. It first appeared in Religion and Medicine: the Moral Control of Nervous Disorders by Elwood Worcester, Samuel McComb, and Isador H Coriat. Though it has a serious use in psychology, it seems to exist mostly to provide an opportunity for people like me to show off weird words derived from classical languages.