The major criticism of jquery comes from its "overhead" which comes from wrapping a lot of functionalities onto relatively(at the time of its onset) large file[1]. While they were legitimate(internet was slow) at the time, at its cost jquery worked as a go-to-solution for browser incompatibility. This was a major issue which jquery solved magnificently.
And frankly, a significant portion of jquery usages are a very limited set of functionalities: selection, class manipulation, some visible on/off, AJAX and promises. A lot of those don't necessarily need jquery[2]. Some hard-core guys go so far as to separately download only modules[3] which works.
Honestly, I wouldn't mind calling a significant portion of jquery to be "pure javascript" as it lets me not worry about browser compatibilities and pleasant stuff that should have been part of standard library. ES6 is supposedly fix most of the complaints, but whether browsers will support them or not is a different question.
It solved problems of cross-browser compatibility back when Netscape was still a thing, before Chrome existed, when major releases of browsers (IE) radically changed functionality between releases, and if I recall, we had Phoenix/Firefox as the most cutting-edge browser of the era. This is what browser market share looked like back then: http://arstechnica.com/uncategorized/2007/02/8908/
When jQuery launched, it appeared on Del.icio.us and Digg, for context of its era: https://jquery.org/history/
(I don't consider jquery a framework, though you can use it like one. Back when browser compatibility was a much larger headache it was a requirement for being productive, but nowadays most browsers implement ES5 reasonably uniformly. Particularly notable are its succinct shortcuts for CSS manipulations, AJAX, and running code on-page-load)
The only real gotcha is that jquery DOM manipulation is not really compatible with native DOM manipulation, but you can get to one from the other
Re: overhead criticisms: the base jquery "runtime" is a pretty reasonable size for the functionality it provides, and the accoutrements are completely optional.
