Cloud Storage is a way to be able to store all of your information remotely, securley, and be able to access it from any computer with an internet connection. It is convenient for sharing files with others, however if computation needs to be done then you must also have cloud computing ability or the files must be transferred to your computer or wherever the computations are done.
You are likely already very familiar with cloud storage such as a gmail account and google docs, icloud, dropbox, and did you know BYU has a university-wide license to box.com for storage? CAEDM also uses a form of cloud storage with your J:/ drive, though this isn't full accessible on the cloud, but it was implemented as a precursor in our college for being able to share files as a group.
Here are some of the common storage methods
Using a list of CAEDM login account names you can create space on the CAEDM J:/ drive that is shared between members of the group. While not fully cloud enabled, you do have access to your group data anytime that you are logged into your CAEDM account. You will notice a directory on your drive that is "J:/groups/" and any groups you belong to will be mapped to that directory. You can read more about setting up and managing CAEDM group accounts here.
Box.com is a popular cloud storage solution used by many private companies that perhaps are not comfortable with all of their data under control by Google. It has a few more configurations that can be controlled by systems engineers, but with that additional control comes additional management and there are a few more restrictions. As BYU has needs now beyond what they wish to manage onsite in their own data centers they have turned to Box (probably has something to do with the church as a whole wanting more control) as a solution to provide all students and faculty unlimited storage, editing capabilities, sharing, collaboration, and more. You can read more about Box storage and how to set this up for your own use if you wish here. There is a video on that page with help for how to quickly get started.
Most of you have probably already used google drive and the accompanying document, spreadsheet, and presentation applications - and there are many others. Each gmail (google) account has 15 GB of free storage associated with it and for a few dollars per year you can increase that substantially. If you have a google account you can just go to drive.google.com, login with your account and explore the options available there. It is easy to share files that others can either view, or edit and collaborate. Recently you can edit Word documents, though full features are not there yet and for that reason OneDrive can be a better option. There is a Google backup and sync application you can download to your computer and then sync selected files directly to your hard drive.
Microsoft also has a cloud storage option and for most options includes Office 365 (Word, Excel, Powerpoint, Outlook) which makes it easy to interact with these traditional and popular office software applications. You can edit in the cloud or from local versions of your software if installed. BYU also has access to this and Office 365 that you may want to learn more about. Besides the University account, which you access with your BYU netid, you can set up your own personal account if you wish. To login and get started go here. Like Google OneDrive has a utility that lets you sync files to your own hard drive if you wish.