Java Servlets & JavaServer Pages (JSPs) form the backbone of Web Application Development in Java. Java Servlet Technology and JSP are a part of the Java Platform, Enterprise Edition (JEE). The latest release of JEE (version 6), which was released a few days ago supports Servlets 3.0 and JSP 2.2. I am not going to emphasize the changes made in these versions here, but a quick Google search should give you an idea on the enhancements made.
A Java Servlet is primarily a class which conforms to the Java Servlet API, a protocol by which a Java class may respond to HTTP requests. A servlet may be used to add dynamic content to a Web Server using the Java platform. The generated content is commonly HTML, but may also be other data such as XML, etc. Similar non-Java technologies are CGI and ASP.NET.