Cells need oxygen for the efficient use of glucose in cellular respiration, the main method most organisms use to gain energy. The oxygen bonds to portions of the glucose molecule, releasing water, carbon dioxide and a large amount of energy. The cells then use that energy to generate adenosine triphosphate, commonly abbreviated as ATP, the main energy currency used by the cell.
Oxygen is used by many cells to process energy resources, and oxygen-based metabolism is the most efficient, but not all cells require it. A few that live in low-oxygen environments do not use it at all, and it is often toxic to these organisms. Fermentation is an example of cells using energy sources without oxygen, but it is far less efficient than cellular respiration.
Oxygen is actually a dangerous chemical in general, and while the cells that use it benefit from it greatly, they must also have defenses against its toxic effects. Oxygen is useful because it reacts strongly with the carbon and hydrogen in glucose, but these are major components of cellular DNA and protein structures as well, all of which can be attacked and destroyed by oxygen. This is particularly true in the case of free radicals, highly reactive singular oxygen atoms that are constantly produced by cellular respiration.