When you switch web site hosts (see also How to change Web Site Host) , you receive a new IP address . The new web site host makes an entry into their nameservers (the machines that translate domain names into IP addresses) that equates your new IP address with your domain name.
The final step in your domain move is contacting the company that you registered your domain with to change their nameserver record to point to your new web site host's nameservers.
If all this happened instantaneously, or even over the course of a few minutes, there wouldn't be a problem. However, the Domain Name System consists of tens of thousands of databases that are distributed across the world. The database update process can take 24 to 72 hours before all the nameservers on the planet know that "yourdomain.com" is now located at a different IP address. (see also Web Site Hosting Options).
During that time, "yourdomain.com" really needs to be in two places (or webhosts) at the same time, because "yourdomain.com" is going to translate into an IP address using the information on the DNS server of whoever is trying to reach your site (or email).
As you can see, it takes time to change webhosts and if you find your webhost isn't a good choice, your site (and email) could be unreachable for days while you scramble to find another!