Let's split it in parts, shall we?
As far as i understood i can "link" several urls with a single web-hosting server
If by that you mean that you can have more than 1 domain name for your web-server; yes you can.
A domain name is something like "www.google.com" for instance.
So I understand that you're asking if you can have two different domain names, like "www.myweb.com" and "some.other-domainname.org" to point to your machine that will be hosting your website.
Yes you can. You should take a look on what a Domain Name System is.
But basically, what a DNS does is translate these names into actual IP addresses.
This is done by having something called a name table that could look like:
"www.google.com" -> XXX.XXX.XXX.XXX (for IPv4 as an example)
"www.youtube.com" -> AAA.AAA.AAA.AAA
Since this is done by some kind of mapping you will also need a static IP address.
Both, static IP adresses and domain names must be bought or rented.
The way the things are connected, they also have to do with the ports where they operate. For instance, http requests operate in port 80 and SSH typically in port 22 if I remember correctly.
So what your web-server would do something similar to this:
listen to port 80 -> read the requested file (specified within the URL request) -> send it through that port 80 along with the http headers and payload as a response.
After that the browser requesting the file would read that http response, parse it and show that info into the actual window of the browser.
And you can also rent a webhosting service.
A webhosting service is basically somebody that already dealt with all of this gibberish and has machines that are ready to serve web content. You only have to upload your website into their webserver.
You can also buy a domain name and make it to point to that rented service