I read a personality description which was based on my star and it was matching with my personality. I want to ask that is it allowed in Islam to read and believe these kind of descriptions ?
It's haram (forbidden). Astrology and horoscopes are considered among "fortune telling", "soothsaying", etc. These are considered as contradicting None in the heavens and earth knows the unseen except Allah (Qur'an 27:65), and stricter scholars interpret belief in astrology as a form of kufr.
Whoever goes to a psychic (`Arraf) or a fortuneteller and believes what he says disbelieves in what has been revealed to Muhammad.
Also astrology is scientifically a load of rubbish:
Where astrology has made falsifiable predictions, it has been falsified.
Astrology and science, Wikipedia