Neon has a very high ionization energy because it possesses a complete valence shell of electrons, making it very stable.
In the electron-dot diagram for neon, all eight electrons fill the second energy level, which is the valence shell for neon. This full valence shell is what gives neon, and other noble gases, their notable stability and inertness. As a noble gas, neon is less likely to lose an electron, resulting in a high ionization energy.
Additionally, as one moves from left to right across a period in the periodic table, ionization energy increases. This is due to the effective nuclear charge increasing as the atomic number increases, strengthening the hold on the valence electrons.
Since neon is on the far right of its period, it has a smaller atomic radius and a stronger electrostatic attraction between the nucleus and the electrons. This strong attraction further contributes to the difficulty of removing an electron, hence a higher ionization energy.