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Zone name servers (also known as root name servers) are servers that maintain a list of every domain's name servers. In summary, they tell web browsers where to find a certain domain's name servers. Then the domain's name servers tell the browser where that domain's website is located by returning an IP address.
When you set or change your name servers, all of the zone name servers around the world must update their lists, which takes time. This is why it might take some time for your name server changes to propagate.