The Java SecurityManager is what allows a web browser to run an applet in its own sandbox to prevent untrusted code from accessing files on the local file system, connecting to a host other than the one the applet was loaded from, and so on. In the same way the SecurityManager protects you from an untrusted applet running in your browser, use of a SecurityManager while running Tomcat can protect your server from trojan servlets, JSPs, JSP beans, and tag libraries. Or even inadvertent mistakes.
Imagine if someone who is authorized to publish JSPs on your site inadvertently included the following in their JSP:
<% System.exit(1); %>
Every time this JSP was executed by Tomcat, Tomcat would exit. Using the Java SecurityManager is just one more line of defense a system administrator can use to keep the server secure and reliable.
A security audit have been conducted using the Tomcat codebase. Most of the critical package have been protected and a new security package protection mechanism has been implemented. Still, make sure that you are satisfied with your SecurityManager configuration before allowing untrusted users to publish web applications, JSPs, servlets, beans, or tag libraries. However, running with a SecurityManager is definitely better than running without one.