"The connection is split up by a device simply.."

A firewall! (or at least a wall)

Imagine you are a packet of data trying to be sent to your computer from outside your network. It looks for a certain IP, say 24.89.12.11, which is your "device". The device splits up the internet connection to many different computers, with internal IP addresses such as 192.168.1.2, 1.3, 1.4, 1.5, and so on. Say your computer is 192.168.1.4.

Now back to imagining you are the packet of data...you are going on your way, dum de dum de dum, when you hit the "device" at 24.89.12.11. Now you are thinking to yourself...do I go to 192.168.1.2, or to 192.168.1.3? What about 192.168.1.4 or 192.168.1.5? Ugh...I don't know! And I can't send it to the wrong computer so...I'll return it to the sender! CONNECTION DENIED.

So you see, even if the "device" is not labelled as or called a firewall, it still acts like one. It has no way of telling the packet which computer to go to.