what does checking off an achievement do? like i completed an achievement so i checked the box that was beside it. But what happens? i'm just curious because i also noticed that my completed achievements don't show up on my profile under the achievements tab. thanks for your help!

It saves them. If you look on the sidebar toward the top, there is a saved section. All of your checked off achievements are found there, so you can access them faster or see which achievements you were working on, etc.

Yeah, completed achievements will have the tiers underneath turn green so you know you've completed them. I use the check marks like mentioned, to save ones that I'm working on or want to remember for some reason. It's easier to keep those all in one place instead of searching through all of the categories to try and find them when I want to see them.