"Your all-time longest streak was105days. That's longer than 96% of other players".

What is the meaning of this?

Longest streak means how many consecutive days you played a chess game. You played a chess game (unrated or rated counts as do bots or variants) every day for 105 days in a row.

96% of chess.com members have a streak less than this.

Does it mean that I have played everyday for 105 days i.e., for more than three months continusously?

Yes, that is what I think it means. Unless the "streak" is referring to something else like the Daily puzzle or perhaps logging in? I think it refers to games each day though.

You should be the one to know where this is from. And that's where the explanation is. It's bizarre to ask others without providing any background.

I think it means logging in. I got like 46, and I have definitely not even played 46 games this year, much less 46 days in a row of playing games

How to see other players year in chess?

I believe it refers to the consecutive days that you logged into the site.

Mine is 165

mine is 86

I think, we can conclude like this :
It will be counted, if we login in a day or play any one in a day like puzzle; any move of 1day/3days/7days game; any game.

I had 47 days straight. My puzzle was 4000 rated top 1% I beat a 2500 like 18 times, I’m top 8% in puzzles for solving 200 something like that and I played a 1007 games played people from 113 different countries which is 47% of the countries in the world,

And I won 436 games online which puts me in the top 5%

i had 105 days too

Mine is 1095 days currently and ongoing .. 
i dont know if i am on top or not

Mine was 119

I first read: your losing streak is 105 days haha