Ionization energy (I.E.) is the energy required to remove an electron from an atom in the gas phase. For example the ionization energy for a sodium atoms is defined as the energy for the following reaction
\[{\rm Na(g) \rightarrow Na^+(g)+e^-}\]
This is actually the first ionization energy as it is the energy required to remove the first electron. The second ionization energy is the energy required to remove an electron from the 1+ ion. For sodium the 2nd I.E. would be
\[{\rm Na^+(g) \rightarrow Na^{2+}(g)+e^-}\]
It is important to note that the each subsequent ionization energy is always higher than the previous one as we are reducing the number of electrons but the number of protons is fixed. Thus, as we remove electrons and decrease the shielding and repulsion, the effective nuclear charge is increasing.
Finally, we can use the Rydberg formula to calculate the I.E. for hydrogen-like atoms since this is the energy need to go from the n=1 state to the n=infinity state.