When you change nameservers or DNS records, the change does not reach the whole internet instantly.
WHAT ACTUALLY HAPPENS
Every internet provider's resolver caches DNS answers for a period defined by the record's TTL. Until that cached copy expires, visitors using that resolver continue to see the old answer. Different providers expire at different times, which is why a site can appear live for you and not for a colleague.
TYPICAL TIMING
Most changes take effect within 1 to 6 hours. Full worldwide propagation can take up to 24 hours, and occasionally 48 for nameserver changes.
WHAT DOES NOT HELP
Clearing your browser cache, restarting your router, or re-saving the record. None of these affect other people's resolvers.
WHAT DOES HELP
Lowering the TTL on a record to 300 seconds a day BEFORE you plan to change it, so the old answer expires quickly. Checking with an external propagation checking tool rather than your own browser. Using your hosts file to preview the new destination immediately.
DURING A MIGRATION
Keep the old site online until propagation completes. Visitors reaching the old server should still see a working site, not an error.