A system of understanding the physical universe that is open to adapting to new information, even if that new information means that what was previously assumed to be true has to be henceforth regarded as false.
Contrary to popular belief, a scientist does not (or at least should not) attempt to prove their theories correct, but rather attempt to find any flaw in the theory, so as to gain a better understanding of the fundamental principal being studied
The difference between Astronomy and Astrology is that Astronomy has undergone numerous changes in the course of its history. Astrology, on the other hand, still suggests that someone born in, say, late October, is a "Libra" when in fact the zodiacal constallation the sun was in when they were born would in fact be Virgo.
This is an easy way of seeing why Astronomy is a science, while Astrology is now mostly relegated to the horoscopes section of the newspaper.