Dvadasi is the twelfth day of the waning or waxing moon (dva, "two," dasi, "tenth"). In the Vedic, lunar calendar, dvadasi follows Ekadasi, a day customarily set aside for exclusive focus on spiritual activity and fasting—at least from grains and beans. Fasting for Ekadasi is considered incomplete unless one breaks fast at the proper time the following day, dvadasi.
Varahadeva is Krishna's boar incarnation. He assumed the form of a boar to lift the drowning planet Earth from the Garbhodaka Ocean with His tusks. The demon Hiryanyaksha had thrown the planet Earth into this ocean, but the Lord stabbed the demon with His tusks and saved the Earth.