Business issues represent major business objectives that users process and report on. Business groups represent sub-categories of business issues.
Let's say I want to provide iPhone as an offer to the customer. Here my proposition would be iPhone. To represent my business objective, I will configure 'Sales' as my business issue and group as 'Phones'.
As you said Propositions are stored in a hierarchy that is comprised of business issues and groups.
Propositions are customer-facing offers ( providing a subscription type of $35 per month,600 Minutes, unlimited Text and 1 GB), action taken to provide a service (If customer representative help in assisting customer who raised a request to change the mailing address) and Retention steps (If customer cancel a contract, providing a discount to retain them).
Business issues can be Sales, Retention, Service and so on.
The below examples will help you understand the concepts.