Why do people fast on Ekadashi?

A lunar fortnight has fifteen lunar days, and ekadashi just means “eleventh”. So you get one in the bright half and one in the dark half, about 24 in a year, and 26 when the calendar adds an extra month.

Because a lunar day doesn't line up neatly with your day, Ekadashi can fall awkwardly or be skipped at sunrise altogether. Then you may notice two dates on the calendar, one for Smarta households and one for Vaishnava ones, each following its own rule.

The best-known story is King Ambarisha in the Bhagavata Purana (9.4). He has kept the vow, and is about to break his fast on the twelfth day, when the irascible sage Durvasa turns up as a guest. His dilemma, and how the story is resolved, shows how seriously the tradition takes this fast.

Later came a whole literature of Ekadashi praise. These are attributed to works such as the Padma Purana and the Bhavishyottara Purana, including the story of Utpanna Ekadashi in which a goddess born from Vishnu defeats the demon Mura. Traditional lists give each of the 24 Ekadashis its own story, rites and promised result, and its own name, though one name, Putrada, is used twice. Texts also give grains as what to avoid, with various reasons, though we couldn't verify the specific passages.

For a devout household, a fast every two weeks sets a rhythm. It's a recurring moment to think about something other than the next meal, with reminders from the people around you. That's an observation about how habits work, not a claim about what the fast achieves.