Every ISP (Internet Service Provider) and web hosting company operates a Domain Name Service. The DNS server translates the domain name into a numerical value that computers on the Internet recognize. The DNS server saves, or caches, previous translations so that later requests can be handled much more quickly (the name server reads the stored information and does not have to perform a translation/search each time the name is resolved). The cache of every DNS server is deleted periodically.
The amount of time DNS caches is based on the TTL (Time to Live) of the record at the time the Caching DNS server last looked it up. Also some caching DNS servers impose their own minimums and maximums which ignore the specified TTL.
To ensure maximum uptime for your site, consider keeping the account at your previous host active for a few days to prevent searchers from going to a nonexistent site.