Amavasya is the new moon day of the lunar calendar. “Pancha Parva Utsavams” or the group of five festive celebrations in Shiva temples are observed every month on five days namely Amavasya (New Moon), Pournami (Full Moon), Ravi Sankramana (Start of a Solar Month), Krishna Paksha Ashtami (8th day of dark fortnight of the lunar month) and Krishna Paksha Chaturdashi (14th day of dark fortnight of the lunar month).

Amavasya is celebrated as a day of cleansing sins and taking a dip in holy water bodies. In line with this, Tirthavari Utsavam is held on Amavasya days in many Shiva temples. 

When a Monday (Somavaram) coincides with Amavasya, it is celebrated as a special Amavasya Soma Pradakshanam. Shula Vrata, one of Lord Shiva's Ashta Mahavrata-s or Eight Great Observances, falls on Amavasya of the month of Thai. 

Amavasya is also the name of a Rishi in the lineage of the Sama Vedic Acharyas mentioned in Vamsha Brahmana. 

Amavasya is also believed to be an auspicious day for remembering /thanking ancestors.

See Also: 
1. Shula Vrata