What are code A and code S?

They are tiers of the Global Starcraft League, held by GomTV in Korea. Players who qualify for Code A (which is inferior to Code S) are considered vastly superior to your average Grandmasters player, even if you can generally find them in GM on the ladder.

From Liquipedia:

The GSL is an elaborate tournament which is separated into two tiers:

• Code S contains the top tier players who are competing against each other to win the GSL.
• Code A contains players who are competing against each other to enter Code S.

You will also hear them mention when someone is or was a Code S champion. This title is considered the biggest there is to win in the SC2 scene, and hence, the current and past champions are always big contenders at other events.