Ok... I dont know how to put this together. But I'll try to explain it the best I can.
Say I have 2 computers. Both of them are connected to the internet on the same connection using a router. Now they all have a lan IP. Ex - 192.168.0.100 and 192.168.0.101. But from the internet, they both have the same IP (the IP assigned by the ISP) (So my router has this IP?).

Now what i want to do this is make a server on one of them and keep the other for regular use. The server will stay online 24/7 listening to, let's say port 1234. So if anyone from the internet type "my_real_ip:1234", they will gain access to the server. But this server's lan IP is 192.168.0.101. And the other computer that I use for normal stuff (192.168.0.100, doesnt stay online all the time).

Is this possible to do? How do I do it?

From router forward port 1234 to the computer that is on 24/7, no problems, it can be done.

I have a Dlink router and it says something about

Can this be about port forwarding?

I would assume so, I have never used a dlink router, check the manual, I'm sure it tells you how to do port forwarding to an internal LAN IP.