Board Game Arena

Why is ELO used, why is it a thing?

It is an indicator of the relative skill levels of players; better players generally have higher ELO. It is self-balancing, changing after each game, so for each player, it will eventually fluctuate around the ELO rating corresponding to their skill level (relative to the field).

Here on BGA, you can use it to filter opponents, avoiding either too weak or too strong opponents. It also serves as a badge of honor, with awards for reaching various ELO thresholds (for each game).

See also wikipedia: https://en.wikipedia.org/wiki/Elo_rating_system
On BGA, they made some changes to the classic formula, more details in this topic: https://boardgamearena.com/forum/viewtopic.php?t=33785

And why it's used, because that let you easily find people of the level you want.

Online, you can find people who play thousands of time the same game. You don't want those player to be against someone who only played a few games.
And personnally I don't have fun playing 2p games with a too big difference of level. If I'm the strongest, it's not interesting, I will take advantage usually pretty fast, and after it's boring. If I'm the weakest, that can be interesting to see how they play (but you can already do it with replays), but usually, most games snowball, and after seeing your first mistake, that's again not interesting.