Hi Derek,
There are three cases that must be considered for your question. I will answer your question directly first, and then mention the other two cases.
Case #1:
Think of “default-information originate” as a safety check. Suppose there was some careless BGP admin that told a router to redistribute some other protocol’s routes into BGP, say EIGRP. If that admin didn’t use a route-map or some other filter, and he didn’t think about that EIGRP was advertising a default route, the consequences could be really bad. You might not want all of your BGP peers to learn a default route from you! As a precaution against this, if you redistribute other routes into BGP and you really intended the default to be included, you must additionally type in “default-information originate.” So in other words, “default-information originate” really has no meaning with BGP unless it is paired with a “redistribute” statement.
Case #2
(config-router)#neighbor 1.1.1.1 default default-originate
What this does is advertise a default route to a specific neighbor. BGP will do this even if it doesn’t have a default route itself (so this is an exception to the rule where you can only advertise networks that are in your routing table).
Case #3
The last case is advertising the default network explicitly like this
(config-router)#network 0.0.0.0 mask 0.0.0.0
Doing this will cause BGP to advertise a default network, but only if you already have the default network in your routing table.
--Andrew