Propagation is a term you'll often hear when working with your domain's DNS settings, but what does it mean?
Anytime you visit a website in your web browser, there is a lot going on behind the scenes to provide you with the requested content. When you load a webpage, your computer first attempts to resolve the domain you are visiting to an IP address. Domain names are a convention created to make websites easier to remember, but your browser needs a numeric address in order to fetch any website data. DNS is what allows your machine to make this translation.
There are many servers involved in translating a domain name into an IP address. Each server involved in the translation process may not be able to provide you with your domain's resolution, but it can tell you which server may have that information. In this fashion, a single DNS request goes from one nameserver to another until it ultimately ends with the nameservers you configured for your domain at your registrar. Once the DNS request makes it to your configured nameservers, an IP address is provided to your local browser and an HTTP handshake begins.
It's well known that a website's DNS information rarely changes. In fact, it only changes when you move your website to a new server or new IP address. Knowing this, a domain's resolution is cached so that the DNS translation does not need to be performed everytime you visit the site. The drawback is that when a change does happen, many DNS servers worldwide need to update their records to reflect the new IP address. It is this process that is refered to as "propagation".
Depending on how close you are to your registrar geographically, this process may finish faster than other locations in the world. For example, if your registrar is located in Washington and you live in California, any DNS update to your site will occur more quickly for you than for someone in, say, China. The closer you are to your registrar, the fewer servers it takes in the chain to serve you the DNS information. Fewer servers have to update their cache and the changes are reflected more quickly for you. This is why we say full DNS propagation may take 24-72 hours worldwide to full update, but if you are within the same country as your registrar, it typically only takes 6 hours.
Want more information? A full explanation of DNS can be found at Wikipedia: