Why is oxygen so important to keep things alive?
Oxygen is used to "burn" simple sugars or fatty acids to produce energy.
Any aerobic cell is going to require oxygen to slowly oxidize the molecules of simple sugars or fatty acids. The energy liberated in these oxidation processes is used to create ATP molecules, that are highly efficient at storing chemical energy. Then the ATP is used wherever the cell requires energy.
In consequence, without oxygen, the cell cannot create ATP, which means it cannot carry out any activity that requires energy. So the cellular activity stops, its structure begins to degrade and the cell dies.