DNS propagation is the time required for DNS servers worldwide to update their cached information for a domain name. It is influenced by the TTL of DNS records that might have changed, but there are also other factors that could come into play.
A DNS change requires up to 72 hours to propagate worldwide, although most often this happens in a matter of hours.
Every time you use a domain name on your computer its DNS information will be stored in cache. This can be local cache on your computer's operating system, DNS cache stored by your Internet service provider, etc.
DNS records are stored in cache mainly to improve performance of DNS queries. Every DNS record has a Time to Live (TTL) value, which is the time DNS servers should store that record in cache. Even if a record is changed, DNS servers will continue working with its formal value from cache until this time has passed.