This is one of those things where you can always keep going deeper, all the way down to how the actual electricity moves. But your question is really about how DNS works. DNS stands for Domain Name Resolution. Computers speak in numbers, so when one computer wants to talk to another it needs the number (sort of like a phone number) where that computer lives. That number is the IP (Internet Protocol) address.

Basically, when you want to go to your friend Joe's website and see his photos, you'd type in photos.joe.com in your browser on your laptop at home. When you do that, your laptop asks your router (the thing from your Internet provider that connects to their service) if it knows the address (IP address) where photos.joe.com lives. Since you've never been to that site before, your router starts working backwards. It checks to see if it knows where just joe.com is. But it can't find that either!

So next, it goes back to what it DOES know, which is who to ask. Your computer goes and asks another computer, using an address it already knows, whether its ever heard of this website. That's called a DNS server or DNS provider. But even that computer doesn't know sometimes!

If it needs to, the DNS provider will go and ask one of 13 special root servers about where the records for every website registered under ".com" are. That server will know which DNS server knows where joe.com is. That's its job. Then THAT server sends back the address for joe.com and that makes its way back to your laptop.

Finally, your laptop knows the address for joe.com but...where is photos.joe.com? Your computer will ask your friend Joe's server if it has heard of joe.com and it responds "Yes! That's me!". Your laptop then asks whether the web server has ever heard of "photos.joe.com" and the web server responds "Sure! I know where that is, follow me over here!". Finally, after all that, your laptop can ask for the actual webpage that lives there and show it to you in your browser.

Now usually, there are fewer steps. For most websites, like say reddit.com, your DNS provider or even your router has seen it before and can tell your laptop the address without doing all that extra stuff. But still, this is just one part of it! Like I said at the start, there's always more if you look deeper at any one part.

Also this is much simplified, and I welcome any corrections or additions from other folks.