Using Dropbox as example as that's a common one:
You have a top-level folder called Dropbox. Under that you have as many folders in as big and as complicated of a folder tree as you want.
The entire structure gets copied onto the Dropbox service, and replicated to any other computers that you have with Dropbox installed.
It's incredibly simple both to set up and to use- literally create an account, download and run a file, copy your existing folders into the Dropbox folder, and that's it. Maybe 5 minutes.