As a kind of geek-translation review, here's what happens when you move a web address:
1) Whois Record/Name Servers
When you register your domain name, you tell the registrar what name servers you're going to use. So if I look up Conquent.com I see two name servers listed:
There are two name servers for redundancy, one that's the primary and one that gets a copy of the address from the primary. So, if I change the numeric address for www.conquent.com from, say 184.108.40.206 to 220.127.116.11, it can take time for the secondary server to get the new address.
2) Your provider's Name Server
Your computer doesn't go directly to NS1.CONQUENT.COM to locate my web site, instead, your computer asks your ISP, such as Comcast. When you look up www.conquent.com you ask Comcast to, in turn, ask NS1. Comcast can cache (or keep a copy) of the old record for up to 24 hours -- so even if you're on a computer that's never visited the website, you still might get the old IP address.
Keep in mind, this is a good thing -- it means that all the people who are visiting sites don't overwhelm NS1.CONQUENT.COM with requests. You visit www.conquent.com on Comcast, it looks up the address, and then your neighbor visits, and Comcast doesn't have to bug us again asking for the same info -- it's part of that redundant system concept that makes the Internet work.
3) Your personal computer DNS cache
Just as Comcast holds onto a copy of the old DNS record, your personal computer holds onto a copy. Restarting your computer can flush the local copies of the old DNS, or you can get geeky and (in Windows), shut down all your browsers, run the Command prompt and type:
but most folks who even have the technical savvy to do this probably won't go to that extent.
Even when I try to translate these concepts into plain English, I know it's still pretty thick. But that's why I say, yeah... it's complicated.