Question: I am reading a book regarding tomcat 7. In a section that shortly explains the architecture of the container he says: "Only one tomcat instance can live in a single Java Virtual Machine(JVM)..." later, the author states: "You can still run multiple instances on same physical box, but as separated Java processes..." What is actually the meaning of running the Tomcat inside of the same physical box, but in a different process?

Answer: 
The physical box is a single computer box. The single computer can have more than one [operating system process](https://en.wikipedia.org/wiki/Process_(computing)) that both run Tomcat. This similar to the way you can have more than one Notepad application open at the same time. Both are open at the same time, and you can interact with either instance. The operating system handles context switching so the same physical box hardware supports more than one process.
Tomcat is basically a Java process like any other. You can run multiple jvm instances on an operating system. If you wish to run a java application twice (like tomcat for example) you can simply do so.
Note that there may be issues of port/addresses collision to consider...