As I remember it, when the partial pressure of O2 drops below that found at an equivalent altitude of 14,000 ft you start to get hypoxic. You can train your way up to higher altitude tolerance, as mountain climbers do, but I think there is a fairly hard limit of around .16 or .14 atm ppO2 in your bloodstream, where you will lose consciousness.
When freediving, there are two limiters--1 is your tolerance for CO2. This is what you normally are running up against when you get the feeling you have to breathe. You can reduce this through training in breathing techniques, that drive down your ppCO2 in the bloodstream so you can go a lot longer before feeling the need to breathe.
It is then relatively easy to push this past the point where you have used up all your O2, and you run into the second limit, which is blackout--i.e. where the ppO2 drops below the threshold required for consciousness. There is an especially dangerous phenomenon called shallow water blackout, which occurs because the ppO2 in your blood is also a function of ambient pressure. At high ambient pressure, say, 2 or 3 or 4 atmospheres, you essentially are multiplying the partial pressure of O2 in your blood by the ambient pressure. You trick your body into thinking you've got a tonne of O2 available when you are deep. On your way back up, the pressure drops quickly, and a pp02 that seemed like way over .14 down deep, quickly becomes much less, and you black out on the way back up, followed by some sinking and drowning if you don't have the proper safety precautions.
So, pure O2 is not even a consideration 1) if you don't know how to get your CO2 down by proper breathing, and 2) if you don't have proper safety in place. You should be learning these things first if you are reading this and considering any kind of freediving. The "Performance Freediving Institute" is one organization where you can at least get the right kind of training to participate in this sport.
Now, there is a serious problem with pure O2--at 20ft depth, you've got your ppO2 over 1.6 atmospheres--and crossing this limit can cause oxygen toxicity. You have so much O2 in your blood it bonds with everything, triggers cascading reactions in your nervous system, and puts you into a seizure. Your esophagus closes, and though you have plenty of O2, you can't ascend because you will embolize. Very dangerous, and we honestly don't have data regarding pure O2 breathup for depth freediving, so we don't know what happens.
We do know that blackouts after static apnea breathholding(breathholds that don't involve depth diving) with pure O2 are more serious than blackouts on air, because your body was used to pure O2, and this creates bigger problems for the body. Its also possible to encourage lung collapse and create other problems. There are other strange effects like the off-phenomenon that are the source of other unpredictable effects in the body... This is not an area to explore without proper research, training, and supervision.
David Blaine did a 20 minute breath hold on O2 on the Oprah show, so it does work. However, I don't recommend messing with it, unless you know exactly what you are doing.