Doing something that is considered "above board" means to be very transparent in how you go about managing a given task or performing a certain action. In this setting, there are no efforts to hide anything that is done along the way, and no attempts to create a false impression regarding the complexity or the nature of the activity. With no efforts to conceal anything or deceive anyone involved, being above board is to display a total expression of honesty that all are free to examine as closely as they like.
The exact origins of the idiomatic expression are somewhat vague, although one particular theory tends to be commonly accepted. Back in the days of seafaring pirates, a common strategy used to deceive the targeted ships was to hide the majority of the pirate crew from the crew of the opposing ship. The idea was to provide the impression that the pirates had no more than a skeleton crew that was barely sufficient to sail the vessel. This would prompt the target to let down their collective guard, making them easier prey for the pirates. Once that guard was reduced, the remainder of the pirate crew would come from hiding, launch the attack and take control of the target ship.
When the crew of a pirate ship chose to not employ this deceptive strategy and would instead have the entire crew within plain sight of the targeted ship, it was said that the crew was above board. The fact that the crew was hiding nothing and no one, and openly displayed their numbers and strength to the opposition meant that no deception was taking place and the target ship knew exactly what type of force would have to be reckoned with.
Over time, this open and honest disclosure of all relevant information came to be known as employing an above board approach. The term is often used in business circles, and is applied to any situation in which the representatives of a company make no effort to spin certain factors or to present facts in the best possible light in order to create a positive impression. When a business is truly above board, all the facts are exposed for the consideration of consumers and business partners, questions are answered directly and fully, and there is no attempt to hide anything to do with a business deal. Honesty of this type is often considered an admirable trait, and may serve as the basis for a consumer choosing to do business with that company for a number of years.