Javascript, for the purposes of this question, is a client-side (in the browser) scripting language.
jQuery is a library/framework built with Javascript. It is very popular because it (nearly universally) abstracts away cross-browser compatibility issues and it emphasises unobtrusive and callback-driven Javascript programming.
AJAX (Asynchronous Javascript XML) is a method to dynamically update parts of the UI without having to reload the page - to make the experience more similar to a desktop application.
EDIT:
It sounds like you're new to this. I would seriously recommend you check out http://www.w3schools.com/js/default.asp to get started. It's what I used to learn javascript and it's done incredibly well.