At a high level, organizational governance at the Apache Software Foundation (ASF) is fairly simple: the Members elect a Board of Directors; the Board appoints various officers and creates PMCs; the PMCs report periodically to the board, and most other officers report through the President, and then to the board.
Existing Members nominate and elect new members periodically, and annually they nominate and elect 9 Directors to the board.
The board appoints operational officers, and delegates responsibility for specific policy or operational areas to each officer. For example, the VP, Legal Affairs Committee is responsible for setting legal policy for the ASF and all Apache projects, and working with corporate counsel.
The board appoints executive officers, including a President, Secretary, Treasurer, etc. who are responsible for specific operations of the ASF.
Most officers report directly to the President on a monthly basis, and the President reports an overall operational status to the board on a monthly basis.
The board creates and updates Project Management Committees (PMCs). In most cases, the board simply ratifies properly constructed requests from the Incubator (to graduate podlings to TLPs), or from the PMCs themselves (to add or remove PMC members). In each case, the relevant PMC has already voted to recommend the change to the board.
PMCs report directly to the board quarterly. The board exercises organizational oversight of PMCs, ensuring that they are functioning as a healthy and meritocratic community, and that they are following Apache policies. The board does not provide technical governance; that is handled within the PMC itself.
The Chair of each PMC is a Vice President of that project, and thus is an officer of the ASF. The primary duty of the chair is to ensure that the project's reports are complete and submitted to the board.
PMCs vote on software product releases. This ensures that all source code releases are acts of the ASF itself, through it's properly governed PMC.
PMCs nominate and elect new committers to their project. PMCs also nominate and vote on new PMC members, which the PMC then recommends to the board that the change be made.
By policy, only individuals may serve as Members, committers, or PMC members or officers. This is one way that the ASF and Apache projects preserve their independence.