The database is stored in a single file that is easily backed up. It does not have any explicit integration with iCloud, but you can easily use it to back up a copy of the db, or you can stream the copy back home yourself via ftp or http.
I'm Kenneth at Realm. As realm databases are files on the phone's file system, you can use the common classes for manipulating them. To do a backup, the NSFileManager class might be useful (the copyItemAtURL method might be what you're looking for). See https://developer.apple.com/library/mac/documentation/Cocoa/... for details.