They call it a "cloud" because when engineers sketched a diagram of a network, they'd draw the workstations, servers, printers, routers, encryption etc. The network would eventually lead to an outside connection (Internet), so they'd show the interior router, firewall, public servers and then an exterior router which would connect to the Internet (a mesh of commercially leased circuits). They'd just symbolize that connection to an image of a cloud to identify an outside connection to the world-wide mesh.
Some goofy marketing twit, however, saw it, thought it looked fluffy and fun...so started to market it.
The cloud in this case is just storage on the Internet; however, I doubt the storage is just oddly dangling somewhere on the Internet but instead securely maintained within the Cox domain. Selling it as "cloud" makes it fluffy and fun so you'll buy this service!