Public holidays can make or break travel days, so check the official holiday calendar for your destination and year before booking, since dates for religious holidays often move annually, some by the lunar calendar. The impact varies by country: in some places holidays mean festive crowds and everything open late; in others nearly everything shuts.
The reliable generalizations: banks and government offices close on public holidays almost everywhere, which matters for visa extensions or currency needs. Public transport usually runs but on reduced schedules. Shops and restaurants depend on the country; tourist areas often stay open while local neighborhoods close. Major attractions sometimes close on the biggest national or religious days, and the days around big holidays bring packed trains, sold-out hotels and surge-priced flights as locals travel home.
My rule of thumb: never plan an arrival, a domestic flight connection, or anything involving officialdom on a major holiday. Either lean into it and enjoy the festivities, or schedule around it. The country's official tourism site lists the dates.