A 501(c)3 nonprofit is essentially a business – one that acts in the public interest and does not need to pay taxes. As such, the decision-making process should be modeled after corporations. So in addition to having officers such as CEO/President, Vice President, you also need a board of directors.
The board of directors (BOD) will make all the decisions that the CEO/President carries out. It is important for private foundations, as well as public foundations, to have one. Private foundations are usually family-oriented, so this results in a lot of IRS scrutiny of their decisions. Therefore, it is advisable that there be at least 2 disinterested (non-family) members on the board of directors that can make decisions in case the family members on the board might need to recuse themselves. Interested family members include siblings, in-laws, parents and grandparents, cousins, aunts, and uncles.
The board of directors are responsible for the direction and the actions of the nonprofit. They can vote to remove or replace the CEO, approve projects, and even vote to dissolve the nonprofit. The full scope of duties for the board of directors can be detailed in the organizational bylaws. As such, they are extremely important to the function of an organization and their actions could be closely scrutinized by the IRS. The directors will have to act in the best interest of the nonprofit and not act to enrich themselves or their family.
In California, organizations are required to have a CEO/President, a chief financial officer, and a secretary. There is no requirement that they all have to be different people. While I generally do not recommend it, there are organizations when all three roles are filled by the same person. The CEO/President runs the day-to-day of the organization as well as carrying out duties tasked by the BOD. The chief financial officer is obviously in charge of the finances. A secretary is, what I believe, the most important job. They are responsible for taking notes and meetings of BOD and officer meetings. This is especially important because the notes will be what the organization and the IRS refers to in the event of an audit.