12 completes a cycle, there are 12 astrological signs, 12 months. 13 restarts the cycle. So it is a number of transformation, of beginning a new cycle or a new round of the spiral. It is a message to let go of the old and allow the new to come in. The number 13 brings the message "don't fear the reaper." Change is not to be feared... it's "bad" only if resisted.
13 is beneficial but it is powerfully transformational and so its meaning depends on the person exposed to its energy resonance. A person who is resisting or unready for the movement may experience it as what is called "bad luck", but in reality so-called "bad luck" is nothing more or less than events that forcibly break up a stagnation. The negative connotation of 13 is false really. Events come with a message and make us move, if we weren't moving of our own volition.
So the meaning of 13 depends on how it is used and how willing we are to connect to change. Notice also that the component digits 1 + 3 = 4, which is "square", a stable foundation. So change has inherent in it the apparently opposite idea of stability and a permanent foundation.
Source: The Kabbalah Centre.