What is the reason that Autobiographer badge is kept in Stack Exchange?
This does not show any participation and people can just fill garbage to achieve this badge.
Is there a reason behind it?
Yes, there is. The reason is explained on the Badges page.
The idea behind bronze badges is to encourage users to try out the different features of the platform and generally explore the site. They are intentionally easy to earn, and therefore having the side-effect that they are easy to game.
In the case of Autobiographer, the point of the badge is for users to see all the fields available on their profile and fill them up. So, even if it is getting gamed, the badge is serving its purpose of creating awareness of the existence of those fields/profile.
All of the badges exist to encourage behaviours that the site owners and community think are good ones. The idea is that you do something once for the badge, which motivates you to learn how to do it, and then since you're basically a good person, once you know how to do it you will continue to do so.
All of the badges suffer to some extent from the possibility of gaming. People will go into a review queue and hit Approve without reading, just to get Custodian. Or do that 1000 times just to get Steward. There is no need to get the "people are doing this just for the badge" number to zero. Instead, you want to get the damage caused by lazy people gaming the badge below the benefit caused by good people starting to do the right thing.
Robo reviewing causes damage. Posting a stupid question just to get 3 downvotes and delete it for Peer Pressure causes damage. What damage is caused by someone's profile being full of
wghjmngsf entries? Really, none. And most people are decent and well meaning, so they will fill it in properly. But if they don't, who does it harm?
I would guess that the badge is simply used to encourage users to share some information about themselves.
Granted it isn't strictly necessary in any real sense, but personally I get a kick out of helping someone and then looking at their profile to find that they're on the other side of the world, or seeing a great answer and checking the profile of the author and finding that it was written by a kid, it gives me hope for humanity.