Gauri is the lord of this day and is good for the cutting of one's hair and nails and shaving.
Shukla Tritya is the name for the 3rd Tithi (lunar day). It's the 3rd Tithi of Shuklapaksha. It's nature is Bala Prada, which can be interpreted as "one that gives power". It's good for following works: first feeding; Upanayana, Deva Pratishta, Manglik (creative, auspicious) works; tonsure, cutting one's hair, nails, shaving; worshipping to something related to water (Apas, Jala); painting, singing, art; education; entering into house; jewellery; works related to animals (horses, elephants), conveyance. Gauri is Devata which rules Tritiya (referring to Muhurta Chintamani and Poorva Kalamrita). Gauri can be translated as "fair-complexioned". It's another name of Parvati, a spouse of Shiva, who's considered to be "a Mother of All", "the one of Mountains" and all other female deities are considered to be her reincarnations or manifestations. As per Brihat Samhita, Shukla Tritiya is ruled by Hari (Vishnu) and all actions done in respect of Vishnu (maintenance, supportive works) are acceptable during this day.