jQuery is a small, fast, feature-rich JavaScript library ('write less, do more') commonly used in web applications. jQuery takes a lot of common tasks that require many lines of JavaScript code to accomplish, and wraps them into methods that you can call with a single line of code. It also simplifies a lot of the complicated things from JavaScript, like AJAX calls and DOM manipulation.
The essence of a jQuery Injection attack is the injection of Javascript code that is run from the client's side on a webpage with the main purpose to alter the website's appearance, manipulate parameters or even to access a user's account.