Hello,
So, lets start off recalling that ionization energy is the energy required to completely remove an electron from a neutral gaseous atom. The trend is that ionization energies tend to increase toward the upper right hand corner of the periodic table where electrons are most tightly held.
The exceptions to this trend occur when ionization of the atom results in an electron configuration with a half-filled or completely filled subshell. Since a half-filled or completely filled subshell is energetically favourable removal of an electron to leave a half-filled or completely filled subshell behind is easier (takes less energy) than you would otherwise expect given the general trend.
Let's look at an example in period 2 of the periodic table comparing N (group 5A) and O (group 6A):
N = [He]2s2 2p3 O = [Ar]2s2 2p4
For nitrogen, the 2p3 subshell is half-filled and the individual orbitals are single occupied as dictated by Hund's rule. Going one step to the right to oxygen adds an electron to our configuration and it must pair with another electron in one of those 2p orbitals. Since a half-filled subshell is energetically favourable and ionization energy is a measure of the energy required to remove an electron from an atom, it follows that it should require less energy (relatively speaking) to remove an electron from oxygen as the configuration of the cation will have a half-filled subshell.
This is analogous to what is happening in for atoms in group 3A. Let's now consider the electron configuration for boron and B+:
B = [He] 2s2 2p1 B+ = [He] 2s2
Removal of the single electron from a higher energy 2p orbital leaves the 2s2 filled. Since filled subshell is energetically favourable it requires less energy to remove an electron from an atom in group 3A and we can see this by its lower ionization energy.
Overall then, when considering or comparing ionization energies you should think about what removal of an electron does to the electron configuration and expect off-trend values for the ionization energies in groups 3A and 6A. Note as well, that removal of an electron from a noble gas should be especially difficult (high ionization E) since they have stable, completely filled shell.
I hope that you find this explanation helpful and happy studying!
Ana