If something is aboveboard, it's done in a completely honest, straightforward way. When a company's business dealings are aboveboard, they act in an honorable, open manner.
It would be nice to think that everyone acts in a way that's aboveboard, but scandals involving money and shady business deals prove otherwise. You might say, "I don't trust that guy — it just doesn't seem aboveboard, the way he avoids answering my questions." This word was first used in the 17th century, reportedly from the idea that it's harder to cheat at cards if you keep your hand above the table, rather than hiding it in your lap.