Arguably, traditional mainframe computing from the 60s-90s was a form of "cloud" service: users logged on via terminals, and the location of that mainframe was of no consequence to the user. The terminals back then (we'll pass over punchcards and tape) were "dumb": typewriter/telex style electromechanical nightmares, then glass teletypes... then along came personal computers - which ran teletype emulation software, to connect with mainframes.
These PC terminals contributed nothing to the mainframe computing effort, and used their local processing capabilities for running interactive local software applications that were not suited to a batch-processing mainframe, such as word processing and spreadsheets. Mainframe owners were obliged to operate draconian security policies about use of their precious resources that were mostly devoted to very boring but vital accounting functions, and where the users' own "creativity" was simply not an option. Connection speeds to mainframes were also laughable by current standards - 300bps was normal, and 9600bps (~"baud") was blistering.And now almost all the main productivity functions such as email, wordprocessing and spreadsheets can be run remotely "in the cloud" via the ubiquitous web-brower interface - and for free - using services such as Google Aps. Yes, you are never quite certain who is going tobe looking at your data, and it is highly likely everything is scanned by the CIA and GCHQ (at least!) but are the spooks really going to be interested in what you or your business is up to?
However, if the idea of sharing resources on the big "public" clouds from Amazon, Google, Apple etc that are being scanned by the spooks bothers you, it is possible to have you own private cloud, since a "cloud" basically comprises raw computing resources, accessible via networks that you mix, match and blend to suit your purpose: processor MHz, memory GBytes and disk Terabytes. Virtual machine software (VMS) is used to wrap these resources into a series of sub-systems that emulate the input and output architectures of microcomputers based on Intel or AMD procesoor architectures - so that standard software operating systems like Unix can be installed and used to create remote computers in this cloud.
Once upon a time there was a discernible performance hit for this type of server hosting, but as Moore's Law proceeds and everything in computing technology just gets bigger and faster, this is now almost imperceptible for web-based business computing applications, and the many benefits of VMS far outweigh the inestimable hassle of operating servers based on discrete hardware.