In some games, the rank above A is S. What does S represent?

S stands for "shuu" (?), which is Japanese for "excellent".

I comes from the usual Japanese grading. Just like how we have A+, A, B, etc. They have their own system which is the same as ours except that instead of A+ they write "S".

I am attending university in Japan and had to have this explained to me because I didn't know what the "S" grade on my grade report was.

There's not a lot of sourced information about the origins of this term, although there's a fair number of plausible explanations:

Originally created in Japan where anything below grade ‘C’ was considered a failure. The 'S-Rank' allowed for a wider range of obtainable grades and thus player motivation.

The TV Tropes term for this is "Rank Inflation:"

But then what about the players who are really looking for a challenge for whom mere golds aren't enough? The solution — give them platinum medals to aim for. A-grade not good enough for you? Go for A+, or S. Sometimes, even these inflated ranks are subject to inflation, with A being about average and the real goal being a more different S rank: SS or even SSS.

Having a rank above "A" also means that it can be somewhat more secret, some extra or additional goal to shoot for. Prior to the widespread adoption of achievements, offering a "S rank" was a way to reward your most devoted players.

I was going to come to the rescue with Gran Turismo, whose S License is higher than B or A (or their variants), and which actually says what S stands for right in the game! And then I looked around for an actual screenshot (well, videos), and discovered that it's not consistent even within this series:

• Gran Turismo 2: "Special"
• Gran Turismo 3: "Super"

Oh well.

According to the Japanese Wikipedia article

?? (Special) ?????? (Superior) ?????A??????????????S??S????

My translation:

With the meaning of Special or Superior, it is used to indicate a position above Rank A. Rank S, Position S, etc.

Special, Secret, or Super are the most common meanings. There's no real reason for it, other than to say something akin to "This is better than good!"