IP means Internet Protocol, and your “IP address” is a set of 4 bytes (numbers) that uniquely identifies your computer on the network. If you go to a command prompt and type “IPCONFIG” (and hit enter of course) it will tell you what IP address your computer is presently using. There are 2 types of IP addresses, static and dynamic. Most internet providers use dynamic addressing. When your computer connects to the internet, it asks your ISP (internet service provider) for an IP address, and the ISP’s computer gives it one to use. Once you log off, the ISP may give that IP address to someone else, which is why it is called dynamic. If you have a static IP address, it’s always the same, no matter what.
Every computer on the internet has a unique IP address. That’s how computers talk to one another (it’s called TCP/IP protocol, which stands for Transfer Connection Protocol / Internet Protocol, and then when we abbreviate it we always add an extra word protocol at the end, don’t ask me why). When your computer tries to access boards.straightdope.com for example, the name means nothing to the computer. It goes through a lookup process and converts boards.straightdope.com to 65.201.198.9 which is its IP address.
As was previously mentioned, by logging your IP address, they are logging what computer you were using when you posted to the board. I believe that most ISP’s these days do keep a log of what IP address is assigned to what computer, just to handle cases of abuse and improper behavior. However, I don’t work for an ISP so I can’t say for sure.
By the way, ISP’s use dynamic addressing because each IP address costs money. If you are an ISP and you have 15,000 customers, but only 1000 of them are ever online at any given time, then it’s much cheaper for you to buy a block of say 5000 IP addresses (gives you some room for expansion) and assign them all as needed (dynamically) instead of buying a block of 15,000 addresses. Some companies buy only a single IP address, and then your computer uses that as it’s gateway to the internet. What this means is that your computer has it’s own IP address that is unique on your computer’s network, but when you actually send a data transfer over the internet the message goes through the gateway computer and uses the gateway’s IP address. This is a lot cheaper for companies, and also helps with the fact that due to the huge increase in the number of computers we are running low on IP addresses to give out to people.
If you posted from a computer in Maine, then you would get an IP address from Comcast, which would be assigned out of the block of IP addresses that Comcast has control over. Then you went to Maryland and used Juno, so you would get an IP address from Juno out of the block of IP addresses that they have control over. If you are doing something particularly naughty, the system administrator of the board looks up your IP address, figures out that it belongs to Comcast, then has to get in touch with Comcast to figure out exactly who you are. Likewise for Juno. At each location, the IP address can be traced back to your user name and whatever info that ISP stores about you (things like which modem you connected on, maybe some personal info about your computer such as it’s network name).