This is not a framework or vendor endorsement, but I liked this simple video explaining ITIL version 3.
It explains the five key IT service cycles by comparing them to business services in a restaurant, as follows:
1) Strategy to headquarters creating restaurant theming
2) Design to chefs developing the restaurant menu (to meet customer needs)
3) Transitions to cooks running the restaurant kitchen (reliably)
4) Operations to waiters/waitresses delivering services (and owning customer satisfaction)
5) Service Improvement to the maitre d' ensuring quality standards
The video is a little quirky in the way it cycles back and forth between ITIL and the restaurant, but overall I think the analogy works!