I think the only times I use it is to go to random articles, which can be quite fun if you're in the mood to discover new things. However,I couldn't tell you a single other function they have on that side bar even with a gun to my head. Just went to check it and apparently they let you print pages out as PDF, news to me. Wikipedia really doesn't advertise its features much.
Like almost every MediaWiki feature, there's a massive pile of Wikimedia drama behind it. They went through at least three major iterations, almost all behind the scenes, for exporting content for offline viewing, including PDF at all stages, and eventually kind of gave up.[1][2][3][4]
This also encompassed the mostly ill-fated PediaPress system to get printed books of wiki content collections, the Collections MediaWiki extension,[5] and various back-end rendering engines that came and went (some without ever being fully deployed in production).
All to have a link that, in the span from OCG to Proton, was made mostly redundant by browsers implementing "Print to PDF".
Ooh! I recently discovered the "Print to PDF" feature too. I used it to print out some pages for offline reading when I took the kiddos on an adventure outside cell network range. It worked really well.
It's actually an obsolescent feature. With modern browsers, you can just use the native "Print page" feature and the content will be styled in a paper-friendly way.