What's that big fat white line for that is on the road right before a stop light?

If you mean the one that runs across the road, it's called a limit line. When the light is red, you're supposed to stop behind it.

Is your problem with the answer provided or people not stopping before the line?

I was aware of what the line meant, but since so many people cross it before they stop, it's apparent that they don't know what it means.

Thanks, kendor - I didn't need my reading specs for that one

Where I am a bunch of people stop well before the white line, leaving space for an SUV and a half. It can contribute to gridlock, since people behind them may not have room to get through the intersection. It mostly seems inattentive and like they have poor car handling skills in either case.

Here is the Uk and European version of Stop lines ,Though the thick type is used for traffic entering a main road from a minor road
They mostly use the thick Stop>Give-way lines (broken)(Yield in Ireland) which you can straddle to gain a better view of traffic and continue when it is safe.But the stop line you Have to remain behind (in theory) But in real life the rule is ignored They are used as a Giveway-Pause... carry on (if safe?) But on the driving test you have to show the examiner you know the rule if asked, or come across them on the test route.
Pics on this page. plus a "Test your Knowledge on the UK Highway Code" Quiz"(Link on right hand side)
www.highwaycode.gov.uk/signs09.shtml