An IP address is a computer's (usually a router's) InterNet address at a given time. IPv4 addresses come in the format ###.###.###.###, from 0.0.0.0 -- 255.255.255.255. IPv6 (the current version of the Internet Protocol) addresses come in the format XXXX:XXXX:XXXX:XXXX:XXXX:XXXX:XXXX:XXXX, from 0000:0000:0000:0000:0000:0000:0000:0000 -- FFFF:FFFF:FFFF:FFFF:FFFF:FFFF:FFFF:FFFF. Most computers only have one IP address, and most IP addresses refer to a single computer at a point in time. For this reason, they provide the closest thing to an identity when users are otherwise AnonyMous.
Most consumers have dynamic IPs, meaning that their IP address can change. However, the ISP which connects people to the InterNet generally stores the MacAddressX associated with a given IP, so you are not anonymous to them, even if your public internet address changes.
Your IP is logged when you make edits to ThisWiki or post on IyagiBbs. Your IP is also logged when you visit nearly any webpage in existence.