It includes services for on-demand computing, storage (in No-SQL form and Blob form), message queueing, service bus, secure connection, identity management, horizontably-scalable relational database, big data computing (Hadoop), media encoding and streaming, content distribution network, reporting, business intelligence, a data marketplace.
The list goes on and on and is increasing rapidly. The gist is, you consume those services, Microsoft hosts and manages them (with high availability, geographic redundancy, etc.) and you pay for what you use.