A unique visitor is a unique address (typically an IP address but usually bundled with other information in case everyone's coming from one IP). A visitor would be perhaps you but if they didn't break it down to unique then you may have 5-10 visits a day. A good unique algorithm will hopefully narrow your 5-10 to 1 'unique' visitor. However, it is actually impossible to get unique visitors unless you use authentication.
The problem with all of these numbers is that they need to be taken with a helluva grain of salt. Unfortunately, they are the best that is available.
Comscore isn't an IP tracking service. It's a recruited consumer panel who agree to share their web surfing habits. It's like Nielsen's TV ratings, but much better from a recruiting and sample quality standpoint.