I have a web server running out of my home. I have assigned it an address such as 192.168.1.123 on port 80.
I understand that this is running on my local network. If
Assuming you have a connection to the internet:
https://github.com/progrium/localtunnel
is a quick way to access your local server from the internet. There might be similar implementations in other languages/platforms. This is just the one I know about.
Remember that security issues need to be carefully considered when opening your local network to the world.