What does the servlet value of 0 (zero) signify?

Short Answer: value >= 0 means that the servlet is loaded when the web-app is deployed or when the server starts. value < 0 : servlet is loaded whenever the container feels like.
Long answer (from the spec):

The load-on-startup element indicates that this servlet should be loaded (instantiated and have its init() called) on the startup of the web application. The optional contents of these element must be an integer indicating the order in which the servlet should be loaded. If the value is a negative integer, or the element is not present, the container is free to load the servlet whenever it chooses. If the value is a positive 128 integer or 0, the container must load and initialize the servlet as the application is deployed. The container must guarantee that servlets marked with lower integers are loaded before servlets marked with higher integers. The container may choose the order of loading of servlets with the same load-on-start-up value.

http://stackoverflow.com/questions/809775/what-does-the-servlet-load-on-startup-value-of-0-zero-signify