The dynamic approach of jQuery allows web pages to be manipulated within the browser, meaning that in just a few clicks, the page can look totally different to the page that was downloaded when initially loading the page.
Functions included as default in jQuery allow developers to animate elements with very little code. jQuery is also easy to extend, allowing developers to create they own functions, set default attributes for the functions, and then call the function, and override the defaults within the scripts. This extendibility allows functions to be written once, an reused wherever necessary.
I use jQuery to run AJAX functions, call functions when triggered by buttons on the website to add interaction to the site, and storing / processing data in-browser on the website.