DNS propagation is the time frame it takes for DNS changes to be updated across the Internet. In other words, it is a period of time ISP (Internet service provider) nodes across the world take to update their caches with the new DNS information of your domain.
Due to DNS caches of different levels, after the nameservers change, some of your visitors might still be directed to your old server for some time, whereas others can see the website from the new server shortly after the change. A change to a DNS record—for example, changing the IP address defined for a specific hostname can take up to 72 hours to propagate worldwide, although it typically takes a few hours. DNS is a vast, distributed system, even the smallest change can take between a few hours and a few days to be propagated across the Internet.