"write less, do more". It's easy-to-use APIs makes the things like HTML document traversal and
manipulation, event handling, adding animation effects to a web page much simpler that works
seamlessly across all the major browsers like Chrome, Firefox, Safari, Internet Explorer, etc.
jQuery also gives you the ability to create an Ajax based application in a quick and simple way.
Big companies like Google, Microsoft and IBM are using the jQuery for their applications.
So you can easily understand how popular and powerful the jQuery is?
There are lot more things you can do with jQuery.
The list does not end here, there are many other interesting things that you can do with jQuery.