The most well known and most frequently used servlet container. Works pretty well for what it does (a pure servlet container), but few, very few people would use this as-is. As a rule of thumb people add tons of libraries to Tomcat (like JSF, JPA, CDI, etc). At some you'll be better off installing a readily made full stack, like the Tomcat based TomEE.
One thing that I really dislike about Tomcat is that it copies the context.xml from a war when it first encounters a particular war and stores it internally. If you deploy a new war with a new context.xml, Tomcat will continue using the old one. The Tomcat developers are a HUGE fan of this feature, but I just don't see the point. Why would one ever want to keep the first version of context.xml encountered and silently ignore newer versions?
Nevertheless, this is -the- hallmark for Java based servers, and every Java professional should have Tomcat experience under his belt.