The cloud has changed how many use the internet drastically, especially designers. In the past, we were forced into filling hard drive after hard drive with revisions, inspiration, textures, and every other sort of file needed for work. Then, for collaboration, you either e-mailed these files to a coworker, or dropped off a flash drive.
Now, instead of endless e-mails of different versions of the same project, designers, developers, and clients can all access the newest version, compare it to past versions, provide input, and even make revisions in some cases, all at the same time while only saving the most important files to a physical hard drive.
Of course, there have always been online storage sites, but the largest differences between older storage services and new cloud-based ones is the speed that the information is delivered to others, and the wider accessibility. The cloud uses multiple servers to deliver one set of information, rather than finding the server with the site or image you were looking for and relying on that server alone to return the proper page. It also allows multiple accounts to be able to have access to the same files without having to create a hierarchy of accounts, though you can if you need to.
If you don’t understand how the cloud works, I suggest checking out Rob Toledo’s article at Vandelay Design. The cloud is revolutionizing the internet, yet again, and if you ignore it you will be left behind.