Expiry is the last day a futures or options contract trades. After that day it stops existing and settles. Open positions are closed at the settlement price.
On NSE, Nifty contracts expire on Tuesday. On BSE, Sensex contracts expire on Thursday. If the expiry day is a market holiday, expiry moves to the previous trading day (NSE/FAOP/67775, s.1.14). So a Tuesday holiday means Monday expiry.
Check the exact dates, holiday shifts included, in the Nifty expiry table.