A Script Supervisor is one of those positions that, when you are making something for a very low budget, seems superfluous. It's also one of the jobs on set that can be extremely important. The job of a Script Supervisor is to record every shot, every action, to take notes on the script as it's being shot. They also assign scene numbers that go on the slate. Though in reality the convention of how scenes are numbered is fairly straight forward, Sc 1 Tk 1 -> Sc 1A Tk 1, etc, they can get a little tricky at times and as a camera assistant and later as a director I depended on them to help me keep track of what was happening and most important, what had happened and what was going to happen.
I'm just thinking about that now, I as I sit here, going through all the footage from the last shoot and making retroactive script notes.
As a 2nd AC, especially on a film or series, you tend to work very closely with the script supervisor for a long period of time. I have fond memories of more than one.
UPDATE: As an update, I went trolling through some of the blog rolls of the sites I frequent and came across this blog Script Goddess. If you have some time and are interested, give it a look - watch the film she has posted about sleep and read the piece on Brent - he was a good guy - someone who helped me when I was just starting out. In fact, I'm going to crack open the nut that is my blog roll, over one the left there, and add this one.