How the catalina.home and catalina.base system properties are used?

The presence of those two properties is required only when you want to use multiple instances of Tomcat without having to install the software multiple times, and not wasting disk space.

The first properties (catalina.home) points to the location of the common information, while the other property (catalina.base) points to the directory where all the instance specific information are held.

Normally, when you are running only one instance of Tomcat, the two properties points to the same directory. But when you want to use the same codebase and having two different instances, then you will have to set the catalina.base properties to a directory containing these directories: /conf (for server configuration files),
/logs (for standard log and output files),
/webapps (for the web applications that will be automatically loaded),
/work (temporary working directories for web applications)
and /temp (used by the JVM for temporary files [java.io.tmpdir]).