Vedic system of Astrology, originated from the ancient days of Modern India. It is an extension of the Vedas. Vedas are related to the learning and understanding of our lives, the reality of nature and how everything becomes part of this grand scheme of Universe. Vedic Astrology is the analytical part of the Vedas with which you can analyse your purpose of birth, life path, karmic debt etc. Modern Science says that we are stardust, it means every single atom in our body was once created by the stars. Thus we all are descended from the same source energy. When the source energy gets affected the resultant gets affected as well. With this understanding, it becomes easier to learn and understand how a person is affected by planets and stars.
Vedic Astrology comprises Planets, Zodiac Signs (Rashi), Nakshatras and their Dashas, Yogas, Aspects, Degrees and Karakas (Significations). It not only tells you the future but also the forgotten/hidden past. In the ancient India, Astrology was used in daily lives with the help of Panchanga(m). It'll briefly tell you what sort of works can be done successfully on a given day. Panchanga(m) is based on Sun and Moon's movements everyday.
"There is a famous quote in South India that “a good day can do more than what a good person can”, this means there are different aspects of Astrology at work every day to give indications of everything good, bad and ugly."
On a deeper level, Astrology is more of a facilitator of the soul, hence it is called “Jyotish” in Sanskrit, meaning light of God. Because the final destiny of every soul is Moksha (liberation). Moksha means leaving the lower consciousness by realizing the higher consciousness. One has to follow the righteous path (Dharma) to find his/her resources (Artha) to enjoy the desires (Kama) in order to lead a good life and to attain Moksha. Yet, on the path of attaining this final liberation every soul takes birth (repeatedly) to enjoy the fruits of its own good and bad deeds. This is what is famously called “Karma”.