Let me try to explain to you how this works:
first let's look at the syntax which is as follows
router eigrp [xx]
eigrp stub [ connected | static | redistributed | summary | receive-only ]
Basically, issuing this command makes the router a stub router! Therefore, it will not announce
any networks to any neighbor unless specified in the options given above.
for example, "receive-only" will not announce anything to any neighbor while the "connected" keyword
will only announce the interfaces connected to the stub router itself, hence the name! ;-)
To advertise an external route to EIGRP neighbors, the route has to be inserted in the
EIGRP topology table first, with the "redistribute" command.
Being a stub router that helps a lot in a Hub-and-Spoke kind of network design where the Spokes are branch offices
that have no other routers (or networks?!) other than their connected interfaces. This helps in a sense that if one
of the spokes loses its connected interface for example, it will not query the Hub router for an alternate path! Therefore,
the Hub will NOT query the other spokes! This will help network stability and conserve bandwidth!
BTW, a stub router will not announce or send any advertisement received from one EIGRP neighbor to another.
This is the basics of it! There are some design issues that can create some problems with stub routing such as
redundant paths, etc which will be more complex and create long article to type!!
Hope that help!