"Late" means "coming or remaining after the due, usual, or proper time". "Late check-in" means check-in after the check-in deadline. Usually, airlines would tell you in the reservation confirmation or on their website when is the last time to check in for a flight. For international flights this is usually (from my experience) somewhere close to 1 hour before departure. The deadlines depend on regulatory requirements, time to process the manifest and luggage, and the complexities of the airports (I've seen the same airline having different check-in limits in different airports for the same types of travel).
If you arrive to the check-in counter after the check-in deadline for the flight, the airline may at its discretion still allow you through, but you might need to sign this limited release of liability for the various cases of mishaps that may occur as the result of you being late.