When you are accessing from an external PC, you will be connecting to the router, rather than directly to the server. So you will need to know the outward facing address of the router (eg go to dnswatch
to find your public facing IP).
The other thing you will need to do is forward the particular port that you want from the router through to the server machine on the intranet. This will be in the router settings. It is more secure to just forward just the ports you need rather than directing all traffic to it (unless you are going to take extra care with the server).
You will be directing port 5555 on the router to port 5555 on 192.168.1.103. It is probably TCP traffic, although this depends on the server application you are running (find out if it requires UDP).
In terms of allowing incoming data, it will not be coming from address 192.168.1.1, but from the address of the external machine (even though it is coming via the router, the packet source address will be from the public ip of the client PC; the router attempts to be transparent). So if you are filtering with iptables, you are going to have to allow at least this one external address to initiate incoming packets on port 5555.