Tithi is a Vedic time unit — one-thirtieth of a lunar month, defined as the time during which the Moon's longitude gains 12° on the Sun's. There are 30 tithis per lunar month, 15 in each paksha (waxing = Shukla Paksha, waning = Krishna Paksha). Tithi length varies (between ~19 and ~26 hours) because both Sun and Moon have non-uniform apparent speeds. Festivals and rituals are scheduled by tithi (e.g., Diwali = Amavasya of Kartik; Holi = Purnima of Phalgun).
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Tithi
A lunar day — the time it takes the Moon to gain 12° on the Sun.