What is the significance of Ashadi Ekadashi?

Question

What is the significance of Ashadi Ekadashi (Shukla paksha)? What are we supposed to do on this day?

Answer 1

The similar question was asked by Yudhisthira

Yudhisthira said:

1. Which would be (i.e. is) the Ekadasl in the bright half of Asadha? What is the name and the manner of it? (i.e. in which manner is it observed?) Tell me about it in detail.

Lord Krishna answered this question in detail which can be found in PADMA-PURANA: UTTARAKHANDA: Chapter 53 Devasayani Ekadasi. Here is the brief description of that:

What is the significance of Ashadi Ekadashi(Shukla paksha)?

2-8. I shall tell you (about that Ekadasl) named SayanI which is very auspicious, which gives heaven and salvation, which is great and which removes all sins, merely hearing about which a man would obtain the fruit of a Vajapeya (sacrifice).

Is there a history behind it?

Yes, it's related to Lord Vishnu's Vamana incarnation and Asura king Bali. After sending Bali in neither world, Lord Vamana promised to live in Bali's loka for 4 months (chaturmas) from Dev SayanI (Ashada bright half) Ekadasi to Dev Uthani or Prabodhini Ekadasi (Kartika bright half) Ekadasi:

On that day one of my forms remains resorting to Bali. Another (form) lies on the back of Sesa in the ocean, O great king, till the coming (EkadasI) in Kartika.

What are we supposed to do on this day?

27-37. On that day on which the lord of gods holding a conch, a disc, and a mace sleeps, a man should worship the god holding a conch, a disc, and a mace, and he should especially, with devotion, keep awake at night. (Even) Brahma is not able to measure the religious merit of (i.e. due to) it. O king, he who, in this way, observes this best vow of EkadasI, which removes all sins, gives pleasures and salvation, even though a candala, always lives in my heaven doing what is dear to me.

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Source: PADMA-PURANA: UTTARAKHANDA: Chapter 53 Devasayani Ekadasi

Answer 2

In the scripture Bhavishyottara Purana, god Krishna narrates significance of Shayani Ekadashi to Yudhishthira, as the creator-god Brahma narrated the significance to his son Narada once. The story of king Mandata is narrated in this context. The pious king's country had faced drought for three years, but the king was unable to find a solution to please the rain gods. Finally, sage Angiras advised the king to observe the vrata (vow) of Dev-shayani ekadashi. On doing so by the grace of Vishnu, there was rain in the kingdom.

Reference and detail : https://en.wikipedia.org/wiki/Shayani_Ekadashi