Mostly things which require lot of cross-browser testing and tweaking which I could not possibly write myself as reliable and test so extensively as the jQuery community does. This includes:
$(document).ready(...). Look at the implementation of this function. There are lot of if-else statements checking various browser features.
Position and dimension methods: $(...).offset(), $(...).position(), $(...).width(), $(...).innerWidth() etc. Again, the same story here. Also, they work reliably (or I assume more reliably that I would be able to achieve myself) for special cases such as window and document.
$(...).animate(). The ability to animate elements based on any (reasonable) CSS style.
Also animation chaining and $(...).stop(). Very fluent API.
Event handlers. This is something that every JavaScript library has, and it’s not anything one could not implement himself, but it’s nice to have.
There are also some less favourite features. One of them is function chaining which seems to be the semi-official jQuery programming style. It may impressive at the first sight, but overall, it’s not anything you cannot do using variables and separate statements and in the end, in my opinion, it leads to a less readable code.
Another minor thing which I like less is eagerness of using closures and deeply nested anonymous functions. It may be harder to read such code after a week. It may not immediately obvious where some variables are coming from and what function scopes are. Try to ready some more elaborate jQuery source to see what I mean.
Even though, one of the selling points of jQuery is selectors, I find that I don't need them so often, and if I need any, I usually get by with the basic ones.
Finally, jQuery DOM manipulation has some useful utilities, but overall, I think one could achieve the same with a little bit more (albeit tedious) code. I know I'm most likely oversimplifying, but it does not seem like that there are some serious cross-browser issues.