Krishna Trayodashi is the name for the 28th Tithi (lunar day). It's the 13th Tithi of Krishnapaksha. It's nature is Jaya Prada, which can be interpreted as "one that brings victory". It's good for following works: Alankar, Pratishta, Agnayadhan, marriage, travelling, entering, clothes; war. Trayodashi is also good for all Manglik works except Upanayana, but during Krishnapaksh it is considered to be Galagraha Tithi which according to classical texts should be left in all Manglik elections.
According to most classical texts (Muhurta Chintamani, Poorva Kalamrita, Brihat Samhita, Vasishta Samhita etc.) Kama is Devata which rules Trayodashi, who's is responsible for forming friendships, sensual pleasures and gratification, sexual desire and its fulfillment. Kamadeva is responsible for human's desires, wishes, passions, pleasure of the senses, the aesthetic enjoyment of life, affection, love and other.
Being Jaya (that can be translated as "victory", "advancement") and ruled by Mangala (Mars), 13th Tithi is suitable for following works: war, weapon making, training in army, collection of army, actions or matters related to power / strength, travelling, festival, medicine, trades, houses, flags & conch-shell.
Lagna (ascendant or rising sign) during Krishna Trayodashi becomes Tithi Shoonya (Lagna which is ruined by Tithi) for times when it is Meena (Pisces) or Vrishabha (Taurus). Sometimes instead of Meena Mesha (Aries) is mentioned. Chitra and Swati Nakshatra also becomes Tithi Shoonya if it falls on Krishna Trayodashi. It's considered that all auspicious works done during Tithi Shoonya periods will be destroyed.