Port 6881: BitTorrent
Port 6881 is the traditional BitTorrent port, used by torrent clients to talk to peers.
What runs on port 6881
Early BitTorrent clients listened on 6881 to 6889, and many still default to 6881 for peer connections and the DHT network. Modern clients often pick a random port instead, and many ISPs throttled the traditional range.
On a home network
PCs, Macs and NAS boxes running torrent clients such as qBittorrent or Transmission listen on it, usually with a port forward or UPnP mapping created so peers can connect in.
If port 6881 is reachable from the internet
A torrent client being reachable is how BitTorrent is meant to work, and the port itself is low risk. What it reveals is that you are running a torrent client, and your IP is visible to every peer in a swarm, which is how copyright notices are generated. Keep the client updated, and do not expose its web interface along with it.
How to check whether it is open on your network
Your torrent client's connection settings show its listening port, and your router's UPnP table shows whether it opened a mapping.
To find out whether port 6881 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.