What is DNS?
DNS is the system that turns the address somebody types into the location of the machine that should answer. When you point your own domain at a site, you are adding a record to that phone book. Changes are not instant because the old answer stays cached around the world for a while.
That caching is why a domain change can look broken for an hour and then simply start working, and why it can work for you and not yet for a friend in another country. Nothing is wrong. Different parts of the internet are still holding the previous answer and will let go of it on their own schedule.
The practical advice is to make the change once, correctly, and then leave it alone for a few hours. Repeatedly editing records because it has not taken effect yet is the single most common way people turn a slow change into a broken one.
How long does a DNS change take?
Usually minutes, sometimes a few hours, occasionally up to a day for the last stragglers. It depends on how long the previous answer was set to be remembered for, which was decided before you made the change.