Cloud computing is when you connect to remote servers to do the heavy lifting and calculations instead of doing the work on your local machine
The servers can be located in your building and operated by your company (private cloud) or may exist as virtual machines on a service like Amazon, which rents space on their web of servers.
The old idea of "1 task - 1 server" led to rooms of servers all working at about 10% load. It was a huge waste of hardware and energy
With memory getting cheaper and processors more powerful, it became possible to do what up till then had only been able to happen on the "big iron" mainframes of HP and IBM. Run virtual machines that existed in software rather than hardware.
The one physical server might host a dozen virtual servers, each server doing a task like e-mail or file storage or database.
That was what started it.
Now with high speed global communications, it really does not matter that much where the physical server is.
You hook up to the network and your data is there on your desktop.
That's pretty much it in a nutshell