For the most part, what micco said.
A few additions:
Service Provider Equipment and NAT
The odds are that your provider has put a box in your house (likely 8" x 8" by 2", but it could be any size) that your computer plugs into and this box plugs into some jack that goes to the internet. This is a single box which has a few functions. The most important function in our current context is that it likely does NAT. micco gave a good description of what NAT is and does. NAT gives you an IP address that noone on the Internet can see. When you go to some web site, you’re really going to your NAT device, which then goes to the web site, receives the response and sends it back to you. So from the web site’s point of view, it was visited by the NAT box.
Hardening
What micco said about protecting (referred to as “hardening” in the biz) NAT boxes (and network-connected devices in general) is true, but not really applicable in your case. You likely have only one box, and this box is very specialized to it’s purpose. It’s not configurable by anyone except your service provider. In fact, you can’t even get into it, as your provider will not give you the password. It’s their property, and the way they see things, your internet service begins at the jack that comes out of this device and is connected to your computer.
What a firewall will protect against
NAT is a type of firewall. NAT or any other firewall will protect you against:
Bad guys connecting to your computer and doing malicious stuff, such as stealing your info or destroying your computer. This includes automated worms, such as Code Red (to name one you may have heard of).
What a firewall will not protect against
Firewalls won’t keep you from getting viruses. These are spread mainly by email and downloads of infected programs. The best thing you can do to protect yourself from these is to keep your computer up-to-date with security patches on a regular basis. And of course, don’t run ANYTHING on your computer that you don’t have 100% confidence is clean. When someone sends you that file “hot-lesbians-in-love.exe”, don’t touch it; it’s a trap.
Firewalls won’t keep you from getting hit by pop-ups. These are spread mainly by ugly web sites that install browser plug-ins. The thing is, you’re asked if you want to install them, so any time you see a dialog box asking if you want to install something, ALWAYS respond no.
If you do the basic things I’ve outlined above (get NAT, keep your security patches up to date, don’t run anything you don’t trust, don’t accept any plugin installations), you will likely NEVER run into a security problem. There are of course exceptions, but they are rare. I for example, only do the above and have never had a virus or pop-up or break-in.
What your provider can maliciously do
Well, the fact is, your provider is the only one who can get past your NAT firewall, so technically, you are vulnerable to them. But practically, it’s highly unlikely they would do anything, especially if they’re of any size and reputation. If you are seriously concerned about this, you’ll want to get a second firewall that only you control and put it in place, but for my money that’s a bit extreme.