This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Hot deployment is a term for deploying or upgrading a web application without having to shutdown and restart the application server.
Tomcat is mostly capable of this. There are a few gotchas such as the handling of static variables from classes stored in common or shared directories. Also repeated hot restarts or redeploys will cause a slight memory leak to show.
All in all though, it does a good job. If you need true 24/7 up time and can never afford to shut it down for a moment, then Tomcat also offers clustering capability with session replication so different nodes can be brought down and brought back up without interrupting service to the application.