Propagation is the process where your new name server (DNS) information is spread to all the computers in the world. Until propagation is complete, your domain and emails will not work consistently.
You only have to worry about this when you update your name servers, or when you change a DNS record in your DNS zone file.
Name server changes typically take 0 to 24 hours, but are known to take as long as 48 hours.
DNS zone record changes (A, MX, CNAME) typically take 0 to 4 hours to resolve, but are known to take as long as 8 hours.
There is nothing you can do to expedite propagation. However, you can plan for propagation to minimize the downtime affects. See the related article.
Whois, ping, and traceroute tests cannot indicate when propagation is complete. The only way to be sure is to wait the maximum time (up to 48 hours).
NOTE: Your DNS record changes will never resolve if you make the update in the wrong zone file. Be sure to only make A, MX and CNAME updates to the zone file located where your name servers point. (If your name servers point to Osirion, then you must only update DNS records at the sameĀ Osirion server. If your name servers point to your registrar, then you must only update DNS records at your registrar.)