Wrong section but a remote hose is a coiled pressure hose that connects to your air tank and to the marker via it's ASA.
This allows you to run an airtank off the marker, usually in a pouch, saving weight.
They almost all come with a quick release connector and some come with a slide check as you mentioned.
This device releases pressure from the marker and purges gas from it in order for you to disconnect the remote hose.
When you reconnect the hose the slide is moved forward to repressurise the marker.
It basically helps you to stop having to faff around turning the valve, connected to the tank, on and off between games.
Remotes tend to be used by scenerio players