An airport reference point is the centre point of an airport, located at the geometric centre of all the usable runways. The ARP is computed as a weighted average of the end of runway coordinates.
I don't know which country you are referring to. These are countries that rely on TERPs for instrument procedures.
From the FAA TERPs Order 8260.3D
- Airport reference point (ARP). The official horizontal geographic location of an airport. It is the approximate geometric center of all usable runways at an airport.
Page 2-16: The ARP is used to center the MSA on the airport.
Page 3-7: The ARP is used to determine the distance requirements of remote altimeter settings.
Page 11-5: The ARP is used to align the FAC with a circling only approach.
Page 14-31: The ARP is used to center the VCOA (Visual Climb over Airfield)
Sometimes you just need a single lat/lon for "where this airport, is." The ARP depicts where "the point" for this airport, is on this airport.
Why is that an interesting thing to have on an airport diagram? Dunno, I've never needed it. But I suppose somebody might. Maybe if you were aligning your INS, and you wanted to know if just typing in the airport ID (which pulls the airport coordinates from the data base) would get you close to where you're located, you could compare your location on the airfield with where the ARP is, and decide whether it's worth the trouble or not to measure exactly where you are on the chart. Of course, with GPS available, there's a much easier way to find your exact present position. So maybe the ARP has less utility now than in the days before GPS.