Padmini Ekadasi vrat is observed on Shukla Paksha Ekadasi in Adhika masam or Adhik mahina. Padmini Ekadasi vrat katha is mentioned in the Skanda Purana as a conversation between Lord Sri Krishna and Dharmaraja.
When Pulastya Muni came to Kartaviryarjunas court to rescue the demon Ravana from Kartaviryarjunas prison, Narada asked Pulastya that how Kartaviryarjuna defeated the great demon Ravana who conquered even the heaven.
Pulastya Muni explained the story of Kartavirya (father of Kartaviryarjuna) and Padmini (one of his thousand queens and mother of Kartaviryarjuna). In Tretayuga, Kartavirya married to thousand queens but none of them given him a son who can rule his dynasty.
To get a son, Kartavirya performed severe austerities for ten thousand years but he failed. One of his queens, Padmini, followed him when he was going to forest and met Anasuya (Maha Pathivrata) and asked about a vrata which can bless her and her husband with a great son.
Anasuya revealed the significance and spiritual importance of Adhika masa Ekadashi (Padmini Ekadasi and Parama Ekadasi) which can give salvation to devotees. The couple performed the Adhika Masa Ekadasi vrata by observing fasting for three days – Dasami, Ekadasi and Dwadasi – and awake for whole night chanting Vishnu mantras and stotras.
Lord Vishnu pleased with the Ekadasi vrat of Kartavirya and Padmini and appeared before them. Vishnu requested the couple to ask any boon. The couple asked the Lord to bless with a great son who can not be defeated and destroyed with anyone else than Lord Vishnu. Lord Vishnu blessed them with a great son, Kartaviryarjuna, who conquered the whole world and even defeated Ravana.
The above legend explains the significance, spiritual importance, and merits or benefits of observing Adhika masa Padmini Ekadasi vratam.