I am having a hard time understanding Windows Azure service bus and access control concepts. In layman's terms, what are they? What are they used for?
The Service Bus component of Windows Azure is meant to handle the problems arising from services that are living in multiple networks. Basically, a service bus just makes it appear as if your code is running on a single machine, while in reality it could be running anywhere within the Azure datacenters.
Access Control lets you use "federated authentication for your service based on a claim-based RESTful model. (Sorry, copy&Paste from an O'Reilly book about Azure!)
Basically, when you create an Azure site, application or service, it could be running on any of the thousands of systems within the datacenter. And each of those systems has it's own IP address, it's own network, memory, processor and whatever more. To let them collaborate and to appear as a single system, these two services have been created.
If you want to learn more about Azure, this would be a good moment to buy a book! :-)
Azure is quite complex and service buses and access control are a bit more advanced topics.