The time of birth is what makes an astrological chart unique. Nobody else will have one the same as yours. Occasionally similar, but never identical. Even twins' charts are different from each other. Combined with the other components of data essential for the calculation of an astrological chart - the date and location - your time of birth is a vital piece of information. It makes everything specific to you alone.
For example, if you were to ask someone for their year of birth, there will be millions of other people born in that same year. Ask them which month and you'll narrow it down a bit. Ask them the day and things become much clearer. Ok, you would then know which zodiac sign they were born under, but that wouldn't make them very unique. Find out the location of their birth, at which hour and minute - then you'll have everything you need to calculate their horoscope.
So, what happens next? Using the date, time and place of birth, the planets and points are calculated and a chart is constructed. This is called the birth chart, or natal chart, and it forms the basis for everything the astrologer can tell you - i.e. your personality, how compatible you are with someone else, or what lies ahead in your future. Timing is everything!