When it was created - jQuery definitely made javascript not shittier. Javascript was a mess (or browser support for it) and IMHO the most import jQuery goal was to eliminate of cross-browser incompatibilities [0].
Indeed. jQuery and prototype.js made writing browser-independent JavaScript possible. That was huge. And the early competition between the two made introduced (or at least drove the widespread use of) a lot of browser behavior that's commonplace now. Not to mention Ajax.
[0] https://en.wikipedia.org/wiki/JQuery#Overview