This summary is not the rule. The rule text controls.
Here's a plain English summary of this rule:
The Board of Governors runs the Oklahoma Bar Association day to day. This rule gives them room to handle tasks and duties that aren't spelled out anywhere else in the rules. In other words, they aren't limited to only doing what's written down word for word.
The Board also has the power to look into matters when needed. They can start an investigation on their own if they think it makes sense, as long as it doesn't go against any other rules. They must also investigate anything the Oklahoma Supreme Court tells them to look into.
For everyday bar members, this means the Board has some flexibility to act and make decisions even when a situation isn't directly covered by other specific rules. It also means the Supreme Court has authority over the Board and can direct them to look into specific issues when needed.