Public holidays are one of the best free windows into a culture, and they generally come in two flavours. Civic holidays like national and independence days bring parades, flag displays, official ceremonies, and fireworks. Religious and traditional festivals are the deeper experience: family feasts, temple and church rituals, street processions, special foods that appear only that week, and cities either emptying as everyone travels to their hometowns or filling with celebration, depending on the holiday.
For visitors, a few things are worth knowing. Many of the most beautiful traditions happen in homes rather than public spaces, so an invitation from a local friend or colleague is gold; accept it, bring a small gift, and follow their lead on customs. Public festivities, from lantern festivals to harvest fairs to new year street parties, are usually open to everyone, and respectful participation is welcomed far more often than resented.
Do a little homework on the specific festival: appropriate dress, whether photography is welcome at religious events, and any fasting periods when eating publicly during daylight would be insensitive. Book accommodation early around famous festivals, and expect transport to be packed just before and after.