Why is oxygen important?
With oxygen cut off for a few minutes, the body can't effectively make energy (ATP) and will start shutting down.
Why is getting rid of CO2 important?
If CO2 builds up in the body high enough and for long enough, it can actually put you into a coma. A good way to think about it is that there are actually 3 waste-disposal organs in the body.
1. Intestines - stool
2. Kidneys - urine
3. Lungs - CO2
CO2 is a waste byproduct of the mitochondria doing their work and is just as important to get rid of as what is in urine and what is in stool.
What is Ventilation?
You will often hear people talk about breathing in terms of oxygenation and ventilation. Oxygenation is the breathing in of oxygen, but ventilation is not technically the equivalent word for blowing out carbon dioxide. We actually don't have a good word to specifically mean that. It's a small point, but a conceptually important point:
Ventilation = Air Movement (not the act of blowing off CO2)
Ventilation simply means moving air in and out of the lungs. If this does not happen then yes, you will not be able to get rid of CO2 because air is not moving out of the lungs. But you will also not be able to bring O2 into the lungs if there is no air movement/ventilation so you will not be oxygenating either.
So ventilation is air movement which is necessary for both oxygenation and blowing off CO2 (we really need a noun specifically for blowing off CO2 . . . expulsion?). Put in another way:
Oxygenation CO2 Expulsion
Ventilation is the heading under which both oxygenation and blowing off CO2 fall. Again, it may be a small point, but explicitly defining these terms and how they relate to each other makes understanding mechanical ventilation much more conceptually easy when you first start learning about it.