Your Moon sign, or Rashi, is the zodiac sign the Moon was in when you were born. Your birth nakshatra, or Janma Nakshatra, is the lunar mansion the Moon occupied at that moment. In Vedic astrology both are read alongside the Lagna, and many calculations, from the dasha sequence to daily panchang, start from them.
Use the time from your birth certificate if you have it. If you don't know your birth time, tick the box and the calculator checks whether the Moon changed sign or nakshatra on your birth date.
Everything comes from the same chart calculation used by the Lagna calculator.
The sidereal sign the Moon was in, with its exact degree, its ruling planet, its element and its nature.
The nakshatra the Moon was in, the pada (quarter) within it, and the nakshatra's ruling planet.
If your birth time is unknown, you see whether your Rashi and nakshatra stayed the same all day, and if not, around what time they changed.
If the Moon changed nakshatra or sign within about an hour of your birth time, the result tells you, because a rounded birth time could change the answer.
The Moon is the fastest-moving body in a Vedic chart. It takes about two and a half days to cross one sign, so on more than half of all dates the Rashi is the same from midnight to midnight, while the Lagna changes sign every couple of hours.
The nakshatra is more sensitive. The Moon crosses one nakshatra in about a day, so on almost every date it moves from one nakshatra into the next at some point, and the pada changes about every six hours. That is why the calculator asks for your birth time and, when you don't have it, shows both possibilities with an approximate change time.
Vedic astrology measures signs against the fixed stars. The Lahiri (Chitrapaksha) ayanamsa is the offset used, computed for your birth date.
The zodiac is divided into 27 nakshatras of 13°20′ each, starting from Ashwini at 0° Mesha. Each nakshatra has four padas of 3°20′.
The time zone is worked out for the place and the date of birth, so older births use the clock offset that applied at the time.
Without a birth time, the Moon's position at the start and end of your birth date is used to estimate when it crossed into the next sign or nakshatra. The time is shown as approximate.
For how the Janma Nakshatra is read in a Vedic chart, read our in-depth article.
A chapter on every nakshatra by Prash Trivedi, on Jyotish Medium.