The higher the nuclear charge of protons in the nucleus, the higher is the ionization energy. Because of the higher nuclear charge, the electrons are bound with more force and hence higher energy will be required for their removal. For instance, magnesium has higher nuclear charge (12 protons) as compared to sodium (11 protons). Hence ionization energy in case of magnesium is higher as compared to sodium.
Similarly the I.E. of fluorine is more than that of oxygen. It can be explained as follows.
F (Z = 9; 1s2 2s2 2px2 2py2 2pz1) is having more nuclear charge than oxygen (Z = 8; 1s2 2s2 2px2 2py1 2pz1). In both the cases, the electron has to be removed from the same 2p-subshell. As fluorine is having more nuclear charge than oxygen, it means that the nucleus of fluorine will attract the outer 2p-electrons more firmly than oxygen. Hence, first I.E. of fluorine would be more than that of oxygen.