In plain words
"Swāmi! It is a joy to me to give up my life and reach heaven, but I do not wish to disappoint the people, with nothing resolved for them, and make them grieve. So grant me the chance to come and see my people every year in the month of Śrāvaṇa, on the day of the Śrāvaṇa star," he asked. Out of this love for his people he asked this boon, that he might see his people once a year.
So this Onam is the sign of the people's affection for Bali Cakravarti. On this Onam day all the people of Kerala take an oil bath at daybreak. In Malayalam, Śrāvaṇa has another name, Chiṅgam. That day they put on new clothes, make sweet dishes of every kind, set them on a plantain leaf, offer them first to Bali Cakravarti and then celebrate this Onam in splendour with their kin and friends. In Malayalam they call the new clothes Ōṇappuḍi. They have come to see this as the true meaning of Onam. What does a new garment mean? It is not merely a new garment worn on the body. It has an inner meaning too. Bali Cakravarti put on a new body; just as eternal divinity puts on a new body, Bali Cakravarti, pressed down to the nether world, puts on once a year the body of the people's love for him, and so the śāstra came to regard this as a new garment. Kerala is the land that won the affection and Prema of God Himself. Truly, in those days they went on enjoying Prema and regard in every way.
This land of Kerala has another name too. 'Paraśurāma Kṣetra.' Why did it get this name? Paraśurāma too was an Avatāra. When the kings cut off the head of His father, His mother Reṇukā saw the sight, at a time when her son was not near, and seeing it: "O Rāma! Rāma!" she cried out. For a person whose citta is pure, for a person whose feeling is selfless, however far away and from whatever place he calls, the call is close at hand for them through waves of electric power, through sound waves, through radiant waves. Paraśurāma, wherever He was, heard His mother's voice. Because Paraśurāma had devotion to His mother, He fixed His mind closely on His mother's voice: how many times did she call?