JSP stands for Java Server Pages and it's part of the J2EE specification. That means with JSP your not using a scripting language, but a real object oriented programming language: Java. These days Java is one of the most used programming languages, popular mainly because of its ease of use.
So why should you be building your websites with JSP instead of ASP or PHP? Well, for one, PHP and ASP aren't really scalable. They're good fun when you want to build a small website, with some dynamic features, but they can't handle larger web-applications. JSP can handle large applications, JSP can handle huge applications. Another great benefit is, that once you've got your website running, JSP code is easier to manage because most of it will be good old Java.