There are many different types of services offered under the name of cloud computing - the three most common are described below.
SaaS
This type of cloud computing delivers a single application through the browser to thousands of customers using a multitenant architecture. On the customer side, it means no upfront investment in servers or software licensing; on the provider side, with just one app to maintain, costs are low compared to conventional hosting. Salesforce.com is by far the best-known example among enterprise applications, but SaaS is also common for HR apps and has even worked its way up the food chain to ERP. And who could have predicted the sudden rise of SaaS "desktop" applications, such as Google Apps and Microsoft Office 365?
Utility computing
The idea is not new, but this form of cloud computing is getting new life from Amazon.com, Sun, IBM, and others who now offer storage and virtual servers that IT can access on demand. Early enterprise adopters mainly use utility computing for supplemental, non-mission-critical needs, but one day, they may replace parts of the datacenter. Other providers offer solutions that help IT create virtual datacenters from commodity servers.
MSP (managed service providers)
One of the oldest forms of cloud computing, a managed service is basically an application exposed to IT rather than to end-users, such as a virus scanning service for e-mail or an application monitoring service (which Mercury, among others, provides). Managed security services also apply, as do such cloud-based anti-spam services as AppRiver.
Here is a good, fairly short (~15 min.) video introduction to cloud computing:
And be sure to visit our cloud hosting site