This a very important part of the ceremony usually in a Brahmin Marriage. Immediately after his student-life, the young bachelor has two alternatives before him – Married life ( Grihasta ) or asceticism ( Sanyas ). Being by nature escapist, he prefers the ascetic life to the tribulations of married life.
kAsi is another name for vAranAsi. He therefore ‘makes his way’ to kasi (VARANASI), complete with slippers, umbrella, bamboo fan etc. When the groom is about to begin his journey, On his way, the bride’s father intervenes and advises him of the superiority of married life to ascetic life. He also promises to give him his daughter as companion to face the challenge of life. The bride's brother convinces the groom that there is life beyond education and by marrying his sister he will have a responsibility to come back from kAsi after graduation. The umbrella is to remain with groom, to remind him in the future, of this advice.the real tradition.
As part of traditon added to some fun the groom is literally carried back to the mandapam - "the sacred canopy". From there on, the groom prepares himself for a new chapter in his life as a householder or grihastam. The days of his brahmacaryam are now over and the acceptance of this is all what the snAtakam is about.
However there are different view points on this aspect.
Given below is an observation by Sri. Narayan of Malaysia :
During the wedding ceremony the groom is welcomed as Mahavishnu Svarupaya varahaya ie maha vishnu himself ( or the Siva the equivalent in the Adi Saiva tradition ) and the bride as Lakshmi. Thence , it is imperative he knows no sin, thence he needs to perform a yatra to kashi , submerge in Ganges and comes and does the wedding purified.
In the days of yore , when a man after education takes a yatra like this ( it takes up some months, sometimes a year on foot) , he gets to see the world , otherwise which he would not have been exposed to , thence from Brahmacharya , before moving to grahasta ashrama he come experienced and purified, disiplined ( goal oriented) and fit to take up the challenges of married life. And those days the groom would have been engaged ( nischya dartha) , and proceeds on this yatra and is welcomed back after the father in-law etc after coming back, with this words Maha Vishnu Svarupaya, and given the kanya dhana.
Samnyasa and Grathasta ashrama are both pillars of the society , which is still relevant and have positive contributions to society.This has to be clearly understood.
With Sai's Luv & Best Wishes.
Om Sai Ram.