You've got a confirmed ticket on the 6PM outstation local. The train may wait a few more minutes after 6PM for passengers before departing to the next station. The time between the mentioned departure time and the actual departure time is the grace period.
In insurance a grace period is a specific period of time during which an insurance policy remains in force even if the premium payment is overdue. This gives policyholders a little extra time to make their premium payments without losing coverage along with policy benefits.