If you have built an Arduino web server (e.g. by following the Arduino web server tutorial), you will be able to access your web server on your local network, probably through your ADSL router. But what must be done if you want to access the Arduino server from outside of your home network?
The tutorial on connecting your Arduino web server to the Internet describes how to set up and access your Arduino web server from the Internet via any Internet connected device such as a PC, tablet or smart-phone. This allows you to remotely view and interact with your Arduino web server pages.
An external service such as no-ip can be used as a solution to the dynamic IP address that is usually assigned to the router. This is also explained in the tutorial.