In my experience the fact that you even know the words "Service Broker" makes you an odd duck. (My company uses the heck out of it, BTW... It boggles my mind that it's so unknown to most developers using the Microsoft SQL Server platform.)
Asynchronous processing. Service Broker has a queue-based metaphor and it can execute stored procedures asynchronously when new messages arrive. I gnash my teeth every time I see problems "solved" by the "we'll just poll the database periodically for changes" pattern that could be better-served by Service Broker.
Service Broker performs store-and-forward reliably message delivery inside a single SQL Server instance and between instances (on the same machine or over a network). The inter-instance delivery is particularly nice insofar as that it can use certificates for authentication (which is very nice when you have disparate Active Directory environments in play).
We've built a couple of system that use it and have been very pleased with the results. I can't figure out why it's so obscure. The documentation isn't terrible but it's definitely got a steep learning curve.