(covers information from several alternate timelines)
A monitor, or monitoring, station was was a type of facility capable of scanning its locality and subsequently reporting its findings.
In 2154, a small monitoring station, manned by three Xindi crewmembers, was on a particular moon near Azati Prime. The facility detected and scanned Enterprise NX-01 while the starship was nearby. The ship, however, detected the monitoring station in turn. The representation of the facility was at first extremely dark on the craft's viewscreen, though a night vision view of the monitoring station then provided a clearer perspective. Rather than risk the facility reporting the vessel's presence to the other Xindi once the moon's rotation brought the facility back into communications range, Enterprise destroyed the monitoring station. (ENT: "Azati Prime")
In 2366, in an alternate timeline, monitor stations were a Starfleet outpost which monitored communications transmitted from Federation and Klingon Empire sources. One of the tools available to these space stations were sensor drones. These stations were located in Federation space. Mointor stations alerted the battleship USS Enterprise-D that Klingon battle cruisers had entered their sector. (TNG: "Yesterday's Enterprise")