In Vedic astrology, the birth star of a person (janma nakshatra) is a very important identifier. It is like an astrological ID card without which you cannot gain access to the wealth of knowledge and insight about your past, present and future.
Hence, it is important to find out and remember one's birth star, rashi and lagna always. In fact, whenever you visit a temple for performing a pooja, the priest will ask you for your name, nakshatra and gothram. These details complete your identification for the sankalpam to be performed for the pooja.
The position of the Moon at the time of birth is very important in Vedic astrology. The nakshatra in which your moon is placed at the time of your birth is called your Janma Nakshatra or birth star. The Rashi to which this star belongs becomes your Janma Rashi (or the rashi which is occupied by the Moon at the time of your birth). For example, if the Moon is in Poorvashada-1 asterism when a person is born, this becomes his birth star and Dhanus becomes his Janma Rashi.
Janma Lagna or the Ascendant is the Rashi which is rising in the Eastern horizon at the moment of birth. The Lagna zodiac changes every two hours on any day.