Ionization energy is a measure of how much energy you need to input in order to remove an electron from an atom's outer shell. This becomes easier for atoms that have less valence electron because it brings them closer to having a full out shell by shaving off the one or two extras they have. However, this is harder for atoms that have near full valence electrons since they only need one or two additional electrons to become stable. Fluorine has 7 electrons in its valence shell, so it wants to gain rather than subtract electrons to reach an octet. Barium, on the other hand, has way less and will give up electrons much more 'willingly'. Thus, since it is harder, it takes more energy to remove electrons from fluorine than barium.