A Board of Officers in the British forces was usually convened to establish the facts of an incident or loss and to make recommendations. It was usually chaired at an appropriate level and made its report to the chain of command. A regimental Board of Officers might be headed by the Major who was Second in Command and report to the Commanding Officer, or more seriously to the Brigade Commander. A Board of Officers was convened to investigate the losses of equipment and personal possessions during the retreat to Corunna in 1809, and made recommendations concerning future conduct and the level of compensation to be paid to individual officers.
A Board of Officers could recommend that disciplinary action might be appropriate and could name responsible individuals found to be at fault. Those persons then had the right to defend their actions, decisions and honour before a Court Martial if it came to that. The Board of Officers did not have executive powers to award any punishment, but could recommend sums by way of recompense to the public purse.
I note that you mention the Royal Navy in Nelson's day. A Board of Officers might investigate the loss of a ship through apparent negligence, running aground, or fire; but equally instances of the purchase of substandard vittles or spoiled food and consequent loss to the Admiralty; or indeed mismanagement of funds.
I hope this is helpful. GD