There's a great degree of superstition surrounding the number 13; most of it has to do with religious numerology, the idea that bad things tended to happen when the number 13 was in any wise involved. For example, Judas Iscariot was considered to be the 13th member of Jesus' inner circle (Jesus Himself, and the 12 apostles) - interestingly enough, in most cases where the apostles are named in the New Testament, Judas is listed last. Even more interesting, you flip back to the Old Testament, it talks about the 12 tribes of Israel, that is, the descendants of Jacob's 12 sons - only, things get mixed up a little. See, for his involvement in an attack made on a tribe Jacob had recently made peace with, Levi and his descendants were denied their own nation in the Promised Land; instead, they became the official "priest tribe" of the Israelites, having their own cities within each of the other nations, where they served those nations in regard to spiritual matters. To compensate for this, Jacob adopted his two grandsons from Joseph, granting each of their descendants a nation in the Promised Land and once again bringing the total of the Israelite nations back up to 12. So technically, Jacob had 13 heirs - but the unlucky one, Levi, lost out on his inheritance (though one could argue that being given the perpetual office of the priesthood is a pretty cush gig in and of itself).
That Friday is significant also has to do with Scripture; Friday is understood to be the 6th day of the week, and the last day of the first week in which God did any work on His creation. Being the 6th day, it is associated with man, and mankind in general, the masterpiece of the creation and also that aspect thereof which caused all creation to fall into chaos. Thus, Friday and the number 6 are associated with both the end of creation and humanity's imperfection and sin. And of course, I could go into how the Antichrist is foretold to capitalize on this number in regard to its own, but I'm sure most of you are aware of that one.
Thus, on any given Friday that coincides with the 13th day of a given month, you have these two numerological misfits coming together and inspiring all manner of fear in the particularly superstitious. Frankly, it's just that - superstition. There's nothing is Scripture that specifically states that Friday the 13th is a day to be dreaded. Let's face it, the Gregorian calendar (the one we all go by these days) didn't even exist until about 530 years ago, and while the old Hebrew calendar still observed the idea of the 7-day week, its structure of reckoning months and years was very different, based more closely on the lunar cycle. Never mind specific dates; the Hebrews observed sundown as the beginning of the new day, a practice still observed by the devout, particularly in regard to religious holidays. In light of all this, one figures the whole Friday the 13th superstition is nothing to get hung up on.