Ok, in this case your iMac will be performing as an application server. As such, it will need to be "reachable" from the Internet. This is typically done in one of two ways: 1) It is assigned a static Public IP address, or 2) It is assigned a static Private IP address.
In the first method, your iMac will be like any other publically available server (Web, E-Mail, etc.) To accomplish this, you would need for your ISP to provide you with a static Public IP. You can then configure the AirPort Extreme to allow remote clients to access this server by creating a DMZ for the server. This would fully expose your iMac to the Internet.
In the second method, you would assign the iMac a static Private IP address that is just outside of the default range of the AirPort's DHCP service. You would then configure the AirPort for port mapping. Which ports that will be needed to be mapped will depend on what your application's support tells you.