Stars (and planets) make consistent patterns. Their positions can be used to determine time, date, etc. They were more signifcant during period as no one had yet come up with an explanation that explained all of the heavenly bodies motions (although several theories such as Ptomley's theory of the movement of the spheres and the Copernican explanation were suggested). Also the absence of strong artificial light after dark meant that the display of stars was much more interesting than we currently see (from within a city at any rate)
If you prefer the later Copernican explanation, then it's worth looking at the appendix in Leonard Digges' called "General Prognostication".
It should also be noted that astrology is at the heart of medicine in period, and was quite influential for a lot of important, well educated people (e.g Saint Thomas Aquinas - see Summa Contra Gentiles. There are rumours that Erasmus also occasionally consulted an astrologer).