Cloud computing allows companies to lease rather than buy services such as:
By leasing rather than buying, companies can save money on hardware and software infrastructure as well as managing and maintaining equipment. Small companies and startups can benefit greatly because they can dramatically reduce the cost of startup and expansion; it provides them with a pay-as-you-grow model.
Some of the major cloud providers include:
In addition, there are many other companies that perhaps don't offer cloud services directly, but help with management, security, compliance, etc. The shift to cloud computing is creating lots of new problems that require solutions.
There are many books, websites, and articles written on this subject. To give you an idea of the complexity involved, here is a simple mindmap:
The article at the link below explains cloud computing through a simple analogy to electricity retailers of the late 19th century: