Cloud storage refers to the data storage services available online. Utilising cloud storage means saving your data to an external server, rather than a form of internal memory (like your computer's hard drive or SSD).
You can access cloud storage from most internet-connected devices, but will not be able to access your files if your device is offline.
Cloud storage service providers include Dropbox, Microsoft OneDrive and Google Drive. The storage capacity available to you will depend on the level of your subscription.