When you change hosts you must make a change to your domain name to point to your new host's name servers. While it's any easy step generally, it does create a frustrating period of time called "propagation". Propagation is the time it takes from when you make a change to your domain name until the time it takes for the whole world to see the change. This time usually spans anywhere from 24 to 72 hours.
Why? Well, really simply put - when you made that change, the place you made the change at must tell thousands of other servers around the world that the change has been made. Some servers request change information every 12 hours, some not but every few days. So - DNS servers use sort of a "virtual word-of-mouth" to update one another, and it simply takes a day or so for the news to spread. Is that basic enough for you?