According to the Brahma Purana, this is the day on which Brahma created the world after the deluge and time began to tick from this day forth. This is one of the 3 and a half days in the Indian Lunar calendar called "Sade-Teen Muhurt", who’s every moment is considered auspicious in general to start a new activity.

Gudhi Padwa is especially dedicated to the worship of Lord Brahma. Legend states that this festival is celebrated to commemorate the corronation of Rama after his return to Ayodhya from 14 years of exile. The gudi is a symbol of victory associated with the conquests of the Maratha forces lead by the great hero Chhatrapati Shivaji Maharaj. Gudi is also displayed as they are expected to ward off evil and invite prosperity and good luck into the house.
A bright green or yellow cloth adorned with brocade (zari) is tied to the tip of a long bamboo over which gathi(a type of sweet), neem leaves, a twig of mango leaves and a garland of red flowers is tied. This is then hoisted by placing a silver or copper pot placed in the inverted position over it. Beautiful designs with special powder of soft, white stone (rangolis) are drawn on the floor in front of it.

Ugadi (Kannada: ಯುಗಾದಿ, from yuga+aadi, yuga is era, aadi means
Start. (The start of an era) While the people of Karnataka and Andhra Pradesh use the term Ugadi for this festival. Ugadi is celebrated on a different day every year because the Hindu calendar is a lunisolar calendar. The Saka calendar begins with the month of Chaitra (March/April) and Ugadi marks the first day of the New Year.

The word Ugadi derives from the word Yugadi. 'Yuga' is the word for 'epoch' or 'era', and 'aadi' stands for 'the beginning'. Yugadi specifically refers to the start of the age we are living in now, Kali Yuga. Kali Yuga started the moment when Lord Krishna passed away. Maharshi Vedavyasa describes this event with the words 'Yesmin Krishno divamvyataha, Tasmat eeva pratipannam Kaliyugam'. Some Indian historians date the beginning of Kali Yuga to 3102 BC.

The day, however, begins with ritual showers (oil bath) followed by prayers, and then the eating of a specific mixture of -
Neem Buds/Flowers for bitterness
Raw Mango for tang
Tamarind Juice for sourness
Green Chilli/Pepper for heat
Jaggery and ripe banana pieces for sweetness
Pinch of Salt for saltiness
This mixture with all six tastes (called "Bevu-Bella"( ಬೇವು-ಬೆಲ್ಲ ) in Kannada, symbolizes the fact that life is a mixture of different experiences (sadness, happiness, anger, fear, disgust, surprise) , which should be accepted together and with equanimity.
Later, people traditionally gather to listen to the recitation of the religious almanac (Panchangam) of the coming year, and to the general forecast of the year to come.

Source: Wikipedia