How to Explain "the Cloud" to a Non-Techie

Tonight my cousin called me to ask for help with his business computing class.  The topic was the cloud or blah blah cloud.  He wanted to know what exactly the cloud is.

This really got me thinking.  I work with both private and public clouds daily in my personal life and career, but I couldn't at first define what exactly a cloud was in non-technical terms.

The best analogy I came up with was an apartment complex.  Renters don't need the space or resources of a whole house.  But the landlord could take on the infrastructure (ie the structure, plumbing, electrical) and the maintenance and rent units of housing to the renters.  

Anyone have a better way of explaining it?  How about the differences between public, private and hybrid clouds?