A .cpt file is produced by mdrun at specified intervals (mdrun -cpt), and contains information on all the state variables in a simulated system. In the case of a crash (hardware failure, power outage, etc), a checkpoint file can be used to resume the simulation exactly as it was before the failure. Simulations can also be extended using a checkpoint file.
During the course of a normal mdrun process (provided that it runs for longer than one -cpt interval), two checkpoint files will be written, state.cpt and state_prev.cpt. When extending simulations, use state.cpt; the state_prev.cpt is a backup copy of the previous checkpoint, maintained in case something goes wrong at the current checkpoint. To convince yourself of this fact, you can inspect the contents of a checkpoint file with gmxcheck.