It is 24 hours prior to the timetabled departure time.
If you are flying multiple sectors on the same itinerary then you check in for all flights 24 hours prior to the first flight.
For example ABZ - LHR - JFK you check in for the LHR - JFK flight 24 hours before the ABZ - LHR flight departs.
If you go into 'Manage my booking' on ba.com it will show you exactly what time check-in opens.