Shukla Trayodashi is the name for the 13th Tithi (lunar day). It's the 13th Tithi of Shuklapaksha. 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. all Manglik (auspicious) works except Upanayana.
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 also 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.
During the vedic month Jyaishtha Shukla Trayodashi becomes Maasa Shoonya Tithi, which is considered inauspicious in succeeding in works started during this Tithi. Lagna (ascendant or rising sign) during Shukla Trayodashi also 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 Nakshatras also becomes Tithi Shoonya if they fall on Shukla Trayodashi. It's considered that all auspicious works done during Tithi Shoonya periods will be destroyed.