In the Bible, Jesus celebrated the Last Supper with His 12 disciples, one of whom was a traitor. Since then, 13 has been unlucky, particularly at meal-times. Even today, hostesses will do anything to avoid having that number at table.
It is my understanding that there is plenty of argument over this phrases origins. Not only have I heard the previous answer muted a few times, but also there is the derivation from the bible of the concept of the perfect number (7) and the imperfect number (6), being one less than the perfect number. Therefore some have said that 13 is unlucky cus it is one less than 14 (2x7). (tenuous reasoning I think, but lots of unlikely things are true!