The purpose of many cloud services like Dropbox, One Drive and iCloud is for storing files in order to retrieve them from any device. In other words, you explicitly save documents to the cloud, usually by saving them to a special folder i.e. Dropbox, iCloud, etc., and after that the files reside on the cloud, not on your computer.
As I’ve written about before, other cloud services like Mozy, Carbonite, etc. are for emergency backup purposes, typically backing up your entire hard drive, not for document retrieval from all your devices.
There is a tricky, hybrid way to use the Dropbox and iCloud type services for both document retrieval and automatic backup. There is a little tool called MacDropAny that will link any folder on your computer to one of these cloud services. Once you do this, all the files within the linked folder will reside on both your computer and the cloud service. (As you can probably guess by the name, this tool only works on Macs.)
I link my Documents folder to Dropbox. In this way, when I make changes to a document on my computer it automatically syncs with the copy in Dropbox. For anyone who is lazy about backing up their computer this is an easy way to at least backup the import stuff.
One very important note of caution: make sure you know the amount of data in the folder you link and keep it within the limits of your cloud data plan. I link folders that only contain documents and spreadsheets, no photos, music or movies, which for me, is only a few gigabytes of data.