yes that option starts the Calibre Content Server. I made the point that it is a separate program as it can be started even if Calibre itself is not running.
If you can do the test of connecting to
http://127.0.0.1:8080 via a browser running locally on your PC then that proves that the Content Server is running. Have you tried accessing it via Safari from your iPhone? Note that in this case you will need to use the IP address of the PC on your LAN instead of 127.0.0.1. If that is not working then your firewall is probably blocking access and you will have to work out how to configure your firewall to allow access from outside your PC to port 8080.
If you want to also be able to access your Calibre library when not connected to your home network (i.e. from the public internet) then you need to know how to find out your external IP address and set up port forwarding on your router. The details of this are hardware specific so detailed instructions cannot be given without knowing more about your hardware setup.