Apache Tomcat
Apache Tomcat server is a web server that does everything that the Apache web server dose.
The sever implements Java Servlet and Java Server Pages technologies, that allow you to build web applications.
Dynamic Web Application
Using Eclipse J2EE will allow you to create a new Dynamic Web Application that will use Apache Tomcat.
The Dynamic Web Application allows you to add Servlets and other web content like HTML pages, CSS and son.
WAR file
The WAR file is a Web Archive that can be copied into the webapps directory of a live Apache Tomcat installation. The server will detect that it is there and unarchive it, making it available.