Any time that DNS changes are made (on any level), you need to wait for propagation to complete. Propagation usually takes around 24 hours but is never usually more than 96. During propagation, traffic may come to either location. One person may see the new server while someone else sees the old one. Also, yourdomain.name may work while www.yourdomain.name does not. All of this is normal during propagation.
To speed things up on the internet, the Internet Server Provider (ISP) caches their DNS records. They create their own copy of the master record, and access it locally to search for website, each time someone tries to view it. This procedure speeds up internet activity, reduces the traffic and thus help the ISP work faster.
Each ISP caches the DNS record and updates it every few days. Each ISP has their own standard time frame to update the cache DNS record. This delay from your ISP will prevent you from viewing your website. This process is know as DNS propagation delay. The slow updating of the server cache is called propagation. The DNS information for your domain gets propagated across all server's on the web. After this propagation completes your website will be accessible to everyone on the internet.
In short, DNS propagation depends upon how frequently the DNS master cache nameservers of your ISP are refreshed.