What is it? Basically it is hard drive space on a server or servers located at a remote location(s) where you can store and share files. In some simple cases where security or privacy is of no concern to the user this could be as simple as an FTP directory on a web server some where. This may be fine to distribute software or open documents to a wide audience. Some security is available simply by encrypting or locking those files and sharing the password with your intended audience.
There are file upload servers offering free to low cost storage. They typically do not encrypt anything so it is up to the user to secure those files prior to uploading. You normally just get a URL for each such file for download. Some examples of these are DL.FREE and MEGA. One thing to remember with "Free" is that you have no guarantee your files will always be there when you or someone else needs them.
Serious about your files? For security conscious individuals and businesses the only way to go is a secure cloud storage service with a good reputation. Whether for personal documents and photos or for sharing of business documents and forms that must be accessible from multiple locations by multiple people, there are a variety of services to fit your needs.
What to consider? What do you need to store and from where do you want access is one question to ask yourself. If all you want to store are your family photos and are not particularly concerned about their security but want instant access just go with the Google photo storage and be done with it.
If your needs are more sophisticated look into dedicated cloud storage providers methods to secure your data from unwanted access. For single point of access users like small companies and individuals you may not need some of the more advanced multi-user accounts. Find the easiest solution that meets your needs with only the bells and whistles you really need.
Some services rely on the user to encrypt files locally prior to uploading. Others will encrypt your files on the fly. But be aware of who holds the keys to your files. Always look for and demand "Zero-Knowledge" encryption. You generate and hold your own keys meaning that the provider who is storing your precious and confidential data has no means to open them. It means that even if forced to turn those files over to an authoritarian goverment or in response to a search warrant, those files remain locked and the provider simply could not unlock them even if they wanted to.
If you have to use a service that is not "Zero-Knowledge" perhaps because in your business environment someone else made that decision for you, consider adding your own strong encryption prior to sending files to the cloud. Of course if these must be shared that presents the problem of sharing an additional key or password.
Authentication. Many but not all providers offer an optional two part authentication to access files. You may receive a code sent to your email, SMS or by an audio call to your phone. That could is an extra step in the process to access your files.
A very good, free tool to encrypt files in local folders is Veracrypt. You can create a container, store files then upload container to your cloud. If your cloud is also encrypted you have a double layer of protection that even the NSA could not crack without years of computer time! One caveat is file size and your upload and download speed. If you create a large container ( perhaps 5GB ) and store a small file 1K, you will still be uploading a 5GB file!
Here are some highly rated providers of secure cloud storage.