Here's another site:
http://www.geobytes.com/IpLocator.htm
aaa.bbb.ccc.ddd = IP address
aaa.bbb = ISP address (this is registered with the top boys).
ccc = ISP subnet (they are allowed to have up to 255 subnets for their aaa.bbb number).
ddd = YOUR ip number (again 255 allowed).
So you can see that for each aaa.bbb number, there can only be 255 x 255 unique IP addresses (or users). This is why ISPs may have more than one aaa.bbb address.
DHCP is the ISP's IP management program. An IP address is assigned to you.
This IP address is given a time to live (TTL). It checks your pc every HALF TTL to see if you are still there. Addresses are usually leased for 12 - 24 hours. If you are still online after that time, your address will be renewed for another TTL. And so it goes on.
Its worth noting that "dynamic" IPs (so called because they always change) are still registered with DHCP usually. So this means even a dialup user CAN have the same IP always, as long as the log in before the TTL expires (when it expires, the address is released for ANYBODY eles to use).