The training is conducted in academies, which are buildings dedicated to educate your personnel. The training for the personnel is needed for them to be able to operate more advanced vehicles.

Generally you don't need to train your personnel before having built your 13th fire station, since the more advanced missions needing more specialised vehicles and tactics don't spawn before that. Of course, since some training courses take some time, building academies earlier to train them ahead of the schedule is a good strategy.

Playing in an alliance, you can use the academies of your alliance members or the alliance itself to train your personnel.