Oceanography: What causes oxygen to be used up in deep waters?

The first answer is generally correct, in that the main process that drives oxygen depletion in deep waters of the ocean (and other places) is the consumption of it during decomposition/respiration; mainly by single celled microorganisms (bacteria and archaea). In reality, however, very little organic matter reaches the deep ocean. Current estimates suggest that <1% of all the organic carbon produced by phytoplankton in the sunlit layer makes it to the seafloor. It is also very cold in the deep ocean (<4 degrees C below 1500 m or so). Meaning respiration proceeds very very slowly and on very little useable organic matter. That point made, I think it is really important to be aware of physical processes, such as mixing and ventilation, and how they influence deep ocean oxygen dynamics. If we guess where there is low oxygen in deep waters of the ocean based only on how much organic carbon (primary production) is produced or transferred to depth there, we'd generally be wrong. The major low oxygen zones, termed 'oxygen deficient zones (ODZs)'  in the ocean actually occur where there isn't a huge amount of phytoplankton growth or organic carbon that sinks into the deep sea. The reason these oxygen deficient zones form is because of larger scale circulation 'quirks'. A fraction of the water in the equatorial currents, which bound all the major oceanic gyres, do not reach the surface layer over the same time scales as the water in the rest of the ocean. Since the surface is the only place that ocean water can gain oxygen, via photosynthesis and atmospheric gas exchange, this water tends to become increasingly depleted of oxygen.