In computing terms, "the cloud" has nothing to do with weather. An internet cloud is made up of servers that users access via the internet.
A cloud-based resource requires no special software installed on a computer. It also needs no physical proximity to servers or resources. Anyone with the right permissions can hop online and get started.
What is the cloud?
Think of the cloud as a method rather than an object. Cloud computing involves removing location and/or software demands from users. Instead, a reliable internet connection and proper authentication allow for full access.
A Google executive referred to his company's services by saying they were "in a cloud somewhere" in 2006. His point involved location. Users didn't need to sit in a building with Google's servers down the hall. Instead, those users could be anywhere in the world, and the services would follow them.
It was a new concept back then, but it's not new now.