It pretty much means anything that is not local storage that you can access online now.

If I put a server in my house that has files available to me online, those files are considered being stored in "the cloud" even though they could be in the next room.

If I rent space from Amazon to store on their servers anywhere in the world, that's also the cloud.

I think the most commonly accepted definitions now imply access via the internet, in the past that was not always the case.