Usability. For instance, you always validate on the server side, but if you can use JavaScript to save a long (relatively) wait for sever side validation, you can improve usability. Instead of making the user wait for the server side validation to tell them that their email address is not valid, check it first with the JavaScript, then when it appears they've entered it correctly, check it again on the server.
Similarly, you can add hints to your forms. For instance, say you have a date field where the user needs to enter their birthday. Using jQuery (or any JavaScript for that matter), you can pre-populate the field with the format you want them to enter their date in, say in a lighter text color, and in italics. When the birthday form field gets focus, you can use jQuery (or any JavaScript) to clear out the hint and accept their real input.
I also like how simple jQuery makes Ajax - which can also make your site more usable. Don't make the user wait for another request and page load when you can use Ajax to give the user the information they want on the page they're currently on.
I've been finding that the best use of jQuery for me personally, has been to increase the usability of the site by trying to minimize wait times, page requests, and just general annoyances, like having to fill out the form again after it didn't validate successfully.