Apps that can act as FTP server are:
Wifi FTP Server (free version that wants to sell pro version)
Ftp server (The Olive Tree)
A root directory can be specified that holds the data to be backed up or/and synchronized.
On the other side a FTP client needs to be installed.
curlftpfs mounts a FTP server in a local filesystem
Filezilla (snyc must be done manually, but differences are shown)