Port 873: rsync
Port 873 is the rsync daemon, used to copy and back up files between machines.
What runs on port 873
rsync efficiently copies only the changed parts of files. When run as a daemon it listens on TCP 873 and offers named modules, which may or may not require a password. rsync over SSH, which uses port 22 instead, is the more common and safer way to use it.
On a home network
NAS boxes often run an rsync server for backups between devices; Synology's network backup service uses it. Linux home servers may run it too.
If port 873 is reachable from the internet
An rsync daemon on the internet can expose whole folders, and misconfigured servers without passwords have leaked backups and sensitive files. If you back up between sites, use rsync over SSH or a VPN rather than exposing 873.
How to check whether it is open on your network
In your NAS settings, check whether the rsync service is enabled and whether its modules require a login. RECON's Port Scan will show 873 on devices where it runs.
To find out whether port 873 is open on something in your home, and whether the internet can reach it, the app scans your Wi-Fi from your phone and checks your public address from the outside. It says what it checked and what it could not. Get RECON for iPhone — one-time purchase, no account, nothing leaves the device.