Dispatchers are always active. It's the Content manager servlet that has an active and a standby construction.
Inside the tomcat java stack, you have 2 servlets running. A dispatcher servlet (application server), and a content manager servlet (content manager).
They can be seperated during install if needed. During install, they refer to the naming convention i used in the previous line in brackets.
When an end user starts a report, the gateway sends the request to the first dispatcher in it's configuration.
That dispatcher sends the request to the active content manager.
The active content manager decides (after authentication and authorisation) where the report should be executed, based on the passive load balancing rules it has.
This is all a bit confusing if you only have 1 or 2 servers, that do it all.
Have a look in the installation and configuration guide that comes with the install of BI.
You should find samples of various confiugration possibilities, and pictures to make them clear.