Why is a day and night divided into 12 hours? Why not 10 hours? What is the significance of 12?
There may be other reasons, but the most obvious one is that 12 can be evenly divided by 2, 3, 4, and 6. This makes it easier to work with portions of the day or night. (Similar reasons apply to the 360 degrees for angles, and the 1080 chalakim per hour for computing the molad.)
Wikipedia suggests that the original adoption of a 12-hour day by the ancient Egyptians, et al. may have been related to the 12 lunar cycles in a solar year.
There's also something about the Egyptians tracking the rising of 24 different stars over the course of the day, but it seems to me that the choice of 24 for the number of stars to track was due to the properties of the number, rather than the properties of the stars. Interestingly, the shift from using 36 stars for this purpose to 24 happened at some point during the "New Kingdom," which was also the period in which our Exile in Egypt happened.
The Midrash notes, that the twelve Shevatim correspond to the months of the year, hours of the day, and the different constellations of the sky.