According to Padma Purana,
In Kruta Yuga, there was a demon named Muran. Muran used to trouble all the Devas and mortals. Once, unable to bear the tyranny of Muran, all the devas approached Lord Siva, who directed them to Lord Vishnu. So, all the devas approached Lord Sriman Narayana for help.
Lord Vishnu agreed to help the Devas and went out to battle with Muran. During the long battle, which lasted one thousand light years, Lord Vishnu wanted to rest for a while. Lord Vishnu also realized that Muran could not be defeated using his conventional Shastraas (Aayudham), and a different weapon against Muran is required to defeat him. Immediately, Lord Vishnu entered a cave called Himavati in Badrikaashrama for rest and created a new weapon through his sankapalam. Muran wished to strike Lord Vishnu while he was sleeping, but Lord Vishnu created (Srushti) Shakti - (Lord Vishnu's female energy, not to be confused with Lord Shiva's wife Shakti), which had emerged out of Lord's Thirumeni, assuming the form of a beautiful damsel and reduced him to ashes with one look. When Vishnu arose, he was pleased by the action of Shakti (Lord's female energy) and named this maiden as Ekaadeshi and granted her a boon. Immediately, the maiden said - " Lord! if you want to grant me any boon then kindly grant me the boon of removing sins for all the people who fast on this day." Lord Vishnu granted her the boon and said, people who worship her would reach Vaikunta. Thus, it is said, that vaikunta ekaadeshi is the first ekaadeshi, which is the Dhanurmaasa (Margazhi month) shukla paksha Ekaadeshi.
This day is also celebrated as Gita Jayanti (the day when Lord Krishna gave Bhagavat Gita to Arjuna) and the day of Ksheerasaagara Mathanam ( chuning of milky ocean).
For Sri Vaishnavas, it is a very holy day and should be ideally spent in fasting, prayer and meditation.