Commission on Filipinos Overseas. It is a purely Philippine organization. The intent is to prepare Filipinos for life abroad. Your fiancée will have to attend a CFO seminar after visa approval but prior to departure. They don't really have authority to deny exit, but they can be very difficult and can cause delays by asking for non-standard documents. They have the authority to request just about anything, both about you and your fiancée. It is best to bring every slip of paper you have to CFO. CFO is usually quick and easy, but if you catch them on a bad day or make them angry, they can make things miserable for you. Well, for your fiancée, but that will trickle down to you.
If you were previously married in the Philippines (or registered your marriage there), and CFO figures that out, they will probably ask for a CENOMAR/Advisory of Marriage for YOU. I do not have first-hand experience with that, so I don't want to give advice that might not be accurate. I am not suggesting she lie at CFO, just that she doesn't volunteer that information unless they ask her.
To be clear, CFO is mandatory for to leave the country.