If you want to run the server on your home network and want it also accessible from the internet, you need to set up port forwarding. This differs, depending on your router's make and model, you need to consult your router's manual for details on how to do it. For minecraft, you need to forward port 25565. If you want to use webadmin from the outside too, you need to additionally choose one port (in webadmin.ini) and forward that port as well.
When using webadmin from the outside, it is highly recommended that you use an https version of the page, which means you need to generate a certificate. There are two scripts, one for Windows, the other for Linux. In order for the windows' script to work, you need to install OpenSsl windows binaries, available from https://slproweb.com/products/Win32OpenSSL.html for example (the Light package is enough).
When using webadmin from the outside, it is highly recommended that you use an https version of the page, which means you need to generate a certificate. There are two scripts, one for Windows, the other for Linux. In order for the windows' script to work, you need to install OpenSsl windows binaries, available from https://slproweb.com/products/Win32OpenSSL.html for example (the Light package is enough).