Astrology is the subject which studies and interprets the effects of planets on human life at a personal level. It is firstly the study of the correlation between celestial events, and events on Earth - both mundane (not person-specific) and related to individual lives.
Astrology is a lot more than just your sun sign. Following major factors are considered in analysing horoscopes. As a subject, it has been studied for at least the past 3,000 years and across many cultures.
Throughout history, there have been many notable people who have taken the topic seriously. Such as Johannes Kepler, the famous astronomer. Yet few people know that he was also a lifelong astrologer. Planetary positions at one's birth time & birthplace reflect that person's character, lessons in life, challenges and spiritual path. It is used not only to predict events, but also to gain information about past and present through esoteric technique.
Astrology doesn't change your destiny or predict it or guarantee a future, It only tells us the best possibility of an event to happen, but no guarantees that it will, It gives you a probable road map of life, like you would have if you entered a race with pitfalls, turns, check points.
Astronomy gives position of planets for a birth or event.
Logic is intelligence applied on those positions.
Prediction given based on that intelligence.