Or just run an FTP server on a computer at home, open the appropriate port (you can actually set the server to use any port) in the router, and anyone who knows the login and password can connect to your external IP address at that port and download files.
Or you can just keep them on the cloud and have an app for that cloud on the phone. I have a few files I want accessible to all my devices - dekstop, laptop, phone. So they're on Google Drive, in a private folder, and I have Drive installed on all the devices. On the phone, I have those files set to keep locally (so I can get to them even without an internet connection) but if they change - on the cloud or on the phone - they get synced as soon as I have a connection. The same on the laptop or the desktop, but you don't have to set a file to be accessible locally. Dropbox does about the same thing. (Free cloud storage keeps getting larger - Drive and Dropbox give you 15GB free at the moment.)