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.
Being Jaya (that can be translated as "victory" or "advancement") and ruled by Mangala (Mars), 3rd Tithi of Shuklapaksha is
suitable for following works or actions: weapon making; wars; training
in army, collection of army, any matters related to power or strength;
travelling; festival; medicine; trades; house matters; flags &
During the vedic month Chaitra Shukla Tritiya becomes Swambhuva - Manvadi Tithi, which is considered to be extremely auspicious for any Punya Karma (Japa, Tapa, Dana, Havan, Homa etc.). But it should be avoided in starting of education, Upanayana, marriage, ending of fasts, construction of house and entering thereof; travelling; plantation works. Another Manvadi Tithi for Shukla Tritya comes during month Bhadrapada and is called Rudra Savarni.
During the vedic months Shravana and Phalguna Shukla Tritya becomes Maasa Shoonya Tithi. Lagna (ascendant or rising sign) during Shukla Tritya becomes Tithi Shoonya (Lagna which is ruined by Tithi) for times when it is Makara (Capricorn) or Simha (Leo). All Uttara Nakshatras (Phalguni, Ashadha, Bhadrapada) also become Tithi Shoonya if they fall on Shukla Tritya. It's considered that all auspicious works done during Tithi Shoonya periods won't be successful and will be destroyed.