Google provides a definition:
Modern computing in the age of the Internet is quite a strange, remarkable thing. As you sit hunched over your laptop at home watching a YouTube video or using a search engine, you’re actually plugging into the collective power of thousands of computers that serve all this information to you from far-away rooms distributed around the world. It’s almost like having a massive supercomputer at your beck and call, thanks to the Internet.
This phenomenon is what we typically refer to as cloud computing. We now read the news, listen to music, shop, watch TV shows and store our files on the web. Some of us live in cities in which nearly every museum, bank, and government office has a website. The end result? We spend less time in lines or on the phone, as these websites allow us to do things like pay bills and make reservations. The movement of many of our daily tasks online enables us to live more fully in the real world.
Wikipedia provides a definition:
Cloud computing describes computation, software, data access, and storage services that do not require end-user knowledge of the physical location and configuration of the system that delivers the services. Parallels to this concept can be drawn with the electricity grid where end-users consume power resources without any necessary understanding of the component devices in the grid required to provide said service.
Cloud computing is a natural evolution of the widespread adoption of virtualization, service-oriented architecture, autonomic and utility computing. Details are abstracted from end-users, who no longer have need for expertise in the technology infrastructure "in the cloud" that supports them.
Cloud computing describes a new supplement, consumption, and delivery model for IT services based on Internet protocols, and it typically involves provisioning of dynamically scalable and often virtualized resources. It is a byproduct and consequence of the ease-of-access to remote computing sites provided by the Internet. This frequently takes the form of web-based tools or applications that users can access and use through a web browser as if it were a program installed locally on their own computer.
The National Institute of Standards and Technology (NIST) provides a somewhat more objective and specific definition: