_forward is an internal redirect. Where as _redirect sends a header that tells the client's browser to go to some other URL, _forward tells the Dispatcher to internally redirect the request somewhere else.
If you consider the normal dispatch order of:
preDispatch()
someAction()
postDispatch()
Calling _forward at any point in that progression will cause the following steps to not be executed. So if you call _forward in preDispatch(), someAction() will not be called and so on. If you _forward() in someAction() and you are using the viewRenderer action helper to render your views (you are letting the framework choose what view script to render), then no view script will be rendered in someAction().
When the request is forwarded to the new Controller / Module the entire dispatch process will be repeated there.
You can find out what action is being dispatched by using:
$action = $this->getRequest()->getParam('action');
$action will be the url form of the action so if the method is name 'someKindOfAction', $action will contain 'some-kind-of'. You can do this as well for controllers and modules.