Essentially it's a combination of two different threads of superstition coming together. Firstly that Fridays are unlucky and secondly that the number 13 is unlucky. When these two elements come together they are thought to create a very unlucky day.
Chaucer alluded to Friday as a day on which bad things happen in the Canterbury Tales as far back as the late 14th century ("And on a Friday fell all this mischance"), and there are numerous references in literature to Friday being unlucky.
"It was accounted unlucky for a child to be born on a Friday, unless it happened to be Good Friday, when the event was counterbalanced by the sanctity of the day." (1870)
As for the number 13, the most common supposition is the superstition is based on the Last Supper in Christianity, where there were 13 dining. Since many of the references to 13 as unlucky seem to be around meals and groups, such as if there are 13 people seated together for a meal it foretells that one will die.
There are many popular urban myths and legends as to where the exact origins of Friday the 13th are, and with modern interest in the Knights Templar, they have been featured in some recent theories as to the origins of the Friday the 13th date.
The Knights Templar were a religious and military order founded in Jerusalem 1118 C.E.. Their oath was to protect Christian pilgrims during the Crusades. They gained much fame, power, wealth, and notoriety over the next two centuries while they were a powerful force. Due to their increased power and wealth, King Philip felt threatened, arranging a mass arrest of all the Templar Knights. Once in custody they were charged with blasphemous acts such as spitting on the cross, worshiping Baphomet, and engaging in acts sodomy and other sexual deviancy. Legend has it that the Knights along with their Grand master, Jacques De Molay, were tortured by all the most brutal means available during the inquisition, and eventually put to death. These fateful events took place on Friday, October 13, 1307.
It is not certain, at all, whether or not the story of the demise of the Knights is the true origin of the Friday the 13th superstition in the Western World. What is certain is that for many people this day holds mystical meaning and they believe it is wise to take care.
It seems more likely to me, that perhaps the number 13 was already thought to be a number with mystical meaning and significance, as well as Fridays, and that the execution and other events, have been chosen to be enacted on these days as part of ritual observance.
Is there any seeming accuracy to these superstitions and the superstition of Friday the 13th itself, as the day being actually 'unlucky' in terms of statistically more tragedies occuring?
Not that I could find. However, people's personal experiences with what is unlucky, or lucky, can vary substantially, and should not be discounted.
From personal experience, 13 has been a lucky number for me. Friday's have generally been good days... and I've no memory of an unlucky Friday 13th.