You might also want to take note of the time listed on the WebIP page. This time is updated every time the computer connects to the internet. So, if you called the computer 6 minutes ago and the time listed is very recent, the computer has connected in response to your call.
A unique IP address is needed by all computers connected to the internet. You can think of an IP address like a phone number (a long phone number). To call someone, you need their phone number. Likewise, to contact a computer, you need its IP address.
The dynamic IP address provided by dial-up lines keeps changing. Every time a computer connects with a dial-up line, it can be assigned a different IP address. In this sense, using a dial-up line is like living in hotels -- the phone number keeps changing.
If you have a dial-up line, then maybe you recall having to enter a serise of 4 numbers with periods in between them for a DNS? That's the IP address of the DNS. Your computer will send the DNS names, like "ro.com," and get back IP addresses, like 205.216.92.5. The IP address is then used to contact the other computer. (ro.com really is at 205.216.92.5, by the way).
Just so you know, most computers running web sites have a static IP address -- it doesn't change.