Everytime a computer connects to the internet it'll look up the IP address (regardless what modem you're using, it'll still look up, not memorize it, unless you configured it to be that way). Anyway, when an IP is assigned to a computer, it basically means that the computer is now a part of the whole computernet (AKA internet), where computers communicate with each other.

Now, if someone has your IP (such as a hacker), he'll be able to go inside your computer, because you don't have a firewall. It's basically a spaceship without shields in a huge mass of enemy spaceships.

However, if you have a dial-up modem or if you are sure your IP changes all the time, you're safe. However, when you've got cable or any other modem that allows static IPs, I suggest you to get a firewall.

www.tinysoftware.com <-- Download the free firewall. It works like charm.