IP Addresses -- How exactly do they work?

I know that an IP Address can be, amazingly enough, used as an address of sorts to figure where... whatever you're doing came from.

What I don't know is how that really works. Does it identify your internet connection, your computer, or some combination of both?

I.e. if I had 3 computers at home, and one internet connection, would the IP address be the same for all of them or different when they are connected since they are different computers?

What if you connect at, say, a free wifi hotspot at McDonalds? Does the IP Address have anything at all to identify your computer, or does it just identify McDonalds as where you are connecting from? Is there some way to know which computer (if it was tested again) connected from McDonalds or do all computers there share a set # of ip addresses?

Mostly I was curious if someone who visited a forum using 5 different accounts on one computer would be able to have 5 different IP Addresses by simply taking his computer to different locations to connect.

Thanks

If you had 3 computers at home all connected to the one internet connection their Internet(or External) IP address would all be the same but their Local IP would be different.

Eg your external might be 202.202.202.202

While some of your local ones might be 192.168.1.1, 192.168.1.2, 192.168.1.3

Again if you connected to a free wifi hotspot your external IP would be the same as all the others on that same hotspot but your local would be different.

Thanks! So I guess it is possible, awesome! I appreciate you taking the time to answer.