jQuery is a JavaScript library. That means that it's a collection of reusable JavaScript code that accomplishes common tasks—web developers often find themselves solving the same problems over and over again. Instead of engineering a solution from scratch each time, it makes sense to collect up all those useful bits into a single package that can be included and used in any project. The creators of jQuery have written code to smoothly and easily handle the most common and most tedious tasks we want to accomplish with JavaScript—and they've ironed out all the little differences that need to be worked out to get the code working in different browsers.
It's important to remember that jQuery is JavaScript, not a language of its own. It has all the same rules and is written the same way as JavaScript. Don't let that frighten you away—jQuery really does make writing JavaScript much easier.
jQuery's official tag line is Write Less, Do More. That's an excellent and accurate description of the jQuery library—you really can accomplish amazing things in just a few lines of code. My own unofficial tag line for jQuery is Find Stuff and Do Stuff To It because finding and manipulating different parts of an HTML document is extremely tedious with raw JavaScript and requires lines and lines of code. jQuery makes that same task painless and quick. Thanks to jQuery, you can not only quickly create a drop-down menu—you can create one that's animated and works smoothly in many different browsers.