What is the significance of astrology in Hinduism? I see many famous sages don't really talk much about it, but why Hindus give alot of importance to it?
Astrology is a word related to phalita jyotisha i.e predictive astrology and there are many subdivisions in that as well.
Vedanga jyotisha is not actually astrology because it deals more with positions of stars and planets in the sky. It also deals with seasons and equinoxes and so on. So Vedanga jyotisha is more related to astronomy. It was mainly used to find appropriate time for performing bi monthly, quarterly and many other special vedic yajnas.
As such astrology is not very important as per scriptural point of view.
We dont see many examples in texts like Ramayana or mahabharata where people visit astrologers to discuss their life events and to find solutions for astrologically unfavorable time frames.
However jyotisha was important for conducting ceremonies and hence muhurtam was an important aspect.
In present society it has become more popular and many other things and customs have also gained popularity.