Cloud is a new concept of networking based on something called as Virtualization. Using this concept of Virtualization to provide different kinds of services to Users, small scale to large scale companies.
|Image Courtesy from Wiki which is originally by OmniGroup|
These services are mainly classified into,
1. SaaS -- Software as a Service
2. PaaS -- Platform as a Service
3. IaaS -- Infrastructure as a Service
4. HaaS -- Hardware as a Service
Cloud makes any service available online making users access everything that they need with few clicks.
To understand better, following is a youtube video from IBM's BlueMix Cloud. You can watch this video and see that its so simple to have your own site created on a server to which you can choose hardware configurations.
Enjoy the Video from IBM BlueMix -- CLICK HERE
Also refer to Wiki link for more details and History -- Click Here