What is the difference between Tomcat, JBoss and Glassfish?

Tomcat is merely an HTTP server and Java servlet container. JBoss and GlassFish are full-blown Java EE application servers, including an EJB container and all the other features of that stack. On the other hand, Tomcat has a lighter memory footprint (~60-70 MB), while those Java EE servers weigh in at hundreds of megs. Tomcat is very popular for simple web applications, or applications using frameworks such as Spring that do not require a full Java EE server. Administration of a Tomcat server is arguably easier, as there are fewer moving parts.

However, for applications that do require a full Java EE stack (or at least more pieces that could easily be bolted-on to Tomcat)... JBoss and GlassFish are two of the most popular open source offerings (the third one is Apache Geronimo, upon which the free version of IBM WebSphere is built). JBoss has a larger and deeper user community, and a more mature codebase. However, JBoss lags significantly behind GlassFish in implementing the current Java EE specs. Also, for those who prefer a GUI-based admin system... GlassFish's admin console is extremely slick, whereas most administration in JBoss is done with a command-line and text editor. GlassFish comes straight from Sun/Oracle, with all the advantages that can offer. JBoss is NOT under the control of Sun/Oracle, with all the advantages THAT can offer.

Tomcat is just a servlet container, i.e. it implements only the servlets and JSP specification. Glassfish and JBoss are full Java EE servers (including stuff like EJB, JMS, ...), with Glassfish being the reference implementation of the latest Java EE 6 stack, but JBoss in 2010 was not fully supporting it yet.