Stop lines are happy accompaniments to stop signs and stop lights in the USA. You will never see a stop line without an adjacent stop sign/light, and you will seldom see a light/sign without a line except sometimes in rare cases or where there is a crosswalk only which, in these cases, serves the same purpose.
They take the form of a while line on the pavement, extending from from the curb to the center of the road (in the case of a 2-way street). If they are used in conjunction with a crosswalk then they will be before it and otherwise wil be before any conduit of pedestrian traffic at a corner.
They serve as a guide as to where to stop. Read that last line again. In my home state, and every state I've visited, you stop behind the stop line. This means your car is behind it; not on it, not your front wheels on it, not just slowing down as you go over it -- the front of you car should be BEHIND IT.
Why is this a BFD? Because when people are crossing the street they ususally cross right after the line and in my many years as an exclusive pedestrian I managed to get my shins whacked at least twice by people who think that the placement of the stop line is just a suggestion. It is not. I break this rule some times too, but I shouldn't. Pedestrian shins will thank you if you don't.