The first time a JSP is hit a JSP compiler (called "Jasper" in the case of Tomcat and several other webservers) parses the JSP code and generates servlet code. The servlet code is then compiled into a Java class file and loaded into the JVM by the classloader. All subsequent hits invoke this class and don't need to be re-compiled.
With Tomcat, you can see this generated code by looking in TOMCAT_HOME/work/Catalina/localhost/YOUR_WEBAPPS_NAME/org/apache/jsp.
I assume the terms pre and post translation are referring to the states before and after Jasper compile the JSP code into servlet code.
A good place to test your understanding of this process is in the decision to use the directive <%@ include file=".... or the JSP action <jsp:include.. The former merges the code into the generated servlet before it is compiled. The latter results in both files being generated into separate servlets that each get excecuted at runtime. The output from each gets merged and sent to the browser.