There are several popular legendary stories to explain the foundation of Padwa celebration.
The fourth day of diwali celebrations or the day following the 'Amavasya' is 'Kartik Shuddh Padwa'. According to a famous legend, on this very day the very powerful King Bali comes out of the Patala Lok every year to rule over his kingdom on Bhulok, as per the boon awarded to him by Lord Vishnu. Since then this day came to be celebrated as Padwa in order to honor and welcome the King Bali.
This day is also known by the name of 'Bali Padyami' or "Bali Pratipada". The word "Pratiprada" literally means "below the opponent's foot".
The day of Padwa also has a historic importance, as it is considered to be the day of the coronation of King Vikramaditya as Vikaram-Samvat was started from this day. Gudi Padwa is symbolic of love and devotion between the wife and husband. On this day newly-married daughters with their husbands are invited for special meals and given presents. In olden days brothers went to fetch their sisters from their in-laws home for this important day.