It is the process is cloud computing. Simply put backing up on the cloud means, backing up your data on a remote server's storage (so not on your own computer or external hard drive / USB drive) over a network. Your data can be accessible (privately or publicly according to your settings) at any time from the internet. You can also use a cloud service to exchange large files (several tens of MB).
The benefits of Cloud Storage
Storing files on the cloud can be useful for many reasons. One of the most important benefits of this storage solution: it saves you the purchase & management of your own hardware.
If you use cloud storage to back up your data, outsourcing resources has the added benefit of not having the original & backup copy in one place. This avoids the total loss of data due to fire or theft.