Watching StarCraft: Brood War leagues like ASL or KSL, I see that in the information panel of each player there are maps that under the category "BAN".
What does this this 'ban' mean, exactly?
It's a map ban process.
This occurs in many games. I'm not aware on the specifics of Starcraft; but if it works like other competitive games, it is part of the map choosing process.
In the map choosing process, there is generally a ban phase, followed by a picking phase. First, both sides will choose maps that they do not want to play. Then, after that, they will begin to pick the maps being played from the remaining pool.
In general, this should lead to closer competition. By each eliminating a number of maps, the players can eliminate maps which they believe they are most likely to lose. With both sides doing this, it helps to ensure that the maps being played are the maps that both players feel they have the best likelyhood of succeeding on (which should work out to the closest possible matches if both players pick properly).