When we move an email account or a website to a different host we have to change some numbers. These are referred to as the DNS settings.
You have a domain name such as joebloggs.com. (it's not available, I checked). It has to be parked somewhere. This does not have to be the same place as your website and your email. If fact I would suggest it isn't. I personally use 123-reg.co.uk but I don't use them for anything else other than parking domains.
Following my advice you have arranged to have your website and email hosted by the Joe Bloggs Hosting Company, not part of 123-reg, as far as I know. Now you have to connect your domain name to your website and email, it doesn't happen by itself.
Every computer and device connected to the internet has an I.P. number which identifies that connection uniquely. This is the internet equivalent of a telephone number and a subject for another item.
The computer, or server, your website is hosted on will have an I.P. number. Something like 220.127.116.11. Now we know where to 'point' your domain to for website traffic so we set the domain to go to 18.104.22.168. The same would go for the email, it might be a different number if it is hosted on a different server.
So, we have clicked the button on the new settings, what happens now? Not a lot as far as you will see immediately. What has been set in motion is a process called propagation. This is a sort of domino effect where the new information is passed from one server to the next until every DNS server in the world has the new information. This can take between 12 to 72 hours to complete depending on the changes made. During this period some people trying to view your website for instance will see the old settings, some the new. The same with the email, some will go to the old and some to the new. So it can all be a bit messy while propagation is under way.
So if you had expected these things to be instant I am sorry but that is the way of the World Wide Web.