The oxygen molecule is unusual in having a ground state that has unpaired electrons, and this means it has a net spin of one. Technically the ground state is a triplet. This is unusual because ground states normally have spin zero i.e. they are singlets. For example the $\mathrm{N}_2$ molecule has a singlet ground state.
Anyhow, the non-zero spin of the oxygen molecule causes the ground state to split into a couple of closely separated levels. This type of splitting is known as fine structure. The spacing between these levels is 0.246 meV, which corresponds to a frequency of 59.4 GHz i.e. microwaves with a frequency of 59.4 Ghz have just the right amount of energy to cause transitions between the fine structure levels.
And this is what happens when oxygen absorbs microwaves at 60 GHz. The absorption spectrum is actually very complex because the oxygen molecule changes its rotation as well as jumping between the fine structure levels, so we get a complicated cluster of lines centred around 60 GHz. At atmospheric pressure the lines are broadened by collisions between oxygen molecules and we see only the characteristic broad absorption hump at 60 GHz. To resolve the many lines within this hump requires the absorption to be measured at very low pressures where collisions between the molecules are infrequent.
