What does it mean when you say through nth day does it include the day n Like I am on a vacation through 17th. Does that include that I am joining back on 17th or on 18th?

When you say "through the 17th," it typically includes the 17th as the last day of the period, so you would be returning on the 17th. If you were meant to return on the 18th, it would be specified as "until the 17th" or "through the 16th."