Ancient Hindu literature is full of mythology related to zodiac signs, constellations (also known as Nakshatras) and planets, which explain a lot of astrological rules. However the popular opinion is that the mythology was just a method that our ancient seers used to explain some very complex physical laws, which were beyond the comprehension of common people.
Unfortunately even today's modern science has not been able to fully understand those physical laws behind this ancient method although it's getting there very fast. Our current understanding of the science of astrology lies in statistics and probability. Statistics is the branch of mathematics, which can deal with correlation between two or more seemingly independent events without knowing the cause of that correlation. If in a chart of 1000 people have the same astrological chart then it can be seen that certain astrological rules hold true in 70%-80% of them.
In statistical terms we may say that the occurrence of a specific event in one's life when certain planetary combination exists is "statistically significant". Let's say that you flip a coin 1000 times then the probability of "heads" is always near 50%. Now let's say that you observe the results of flipping a coin during the sun set and sun rise. If you find, after an year long test, that probability of "heads " coming up during sunrise is not actually 50%, as expected, but its 70%, then you can actually construct a rule that if you flip a coin during sun rise, the chances of you getting a "heads" will always be more.
Vedic astrology can be explained in a similar way. Certain combinations in one's chart actually result in a prediction, which turns out to be correct in 70-80% of the charts having that combination. We may not explain it yet as to why it happens but the evidence is pretty strong that events can be predicted with very reasonable statistical significance.