A refresher course first though, Vedic Astrology uses a constellational way to measure zodiac whereas Western Astrology uses the tropical zodiac.
Ancient Hindu literature is full of myths that relate to zodiac signs, constellations (that are known as Nakshatras in Hindi) and planets that explain a lot of astrological rules. However, popular opinion suggests that these myths were just methods that our ancient seers used to explain certain convoluted and intricate physical laws, which were beyond the comprehension of common people.
Unfortunately even though there has been much advancement is Modern Science it still has not been able to fully understand those very physical laws behind this ancient and revered method. The good news though is that we are getting there sooner than later.
Our current understanding of the Science of Astrology stems from the study of statistics and probability. Statistics is that branch of mathematics which deals with correlation between two or more seemingly independent events without previously knowing the cause of that correlation. For instance, if in a chart, 1000 people have the same astrological chart then it can be seen that certain astrological rules hold true in 70-80% of them. So, in statistical terms we can say that the incidence of a specific event in one's life when certain planetary combination exists is "statistically significant".
Let us say that you flip a coin 1000 times. Then the probability of "heads" is always near to 50%. Now let us say that you observe the results of flipping a coin during sunset and sunrise. If you find, after a yearlong test, that the probability of "heads" coming up during sunrise is not actually 50%, as was expected, but it’s 70%, then you can actually construct a rule that if you flip a coin during sunrise, the chances of you getting a "heads" will always be more.
Following that particular stream of thought, Vedic astrology can be explained in a similar manner. Certain combinations that are present in one's chart actually result in a prediction that turns out to be correct in 70-80% of the charts that also have that particular combination.
We might not be able to explain as to why it happens, yet, but the evidence in front of us is pretty consistent that events can be predicted with very logical statistical significance.