During 'regular' photosynthesis water (H2O) is broken down during Oxygen Evolving Complex to leave the individual atoms (H and O) along with protons and electrons which fuel photosynthesis.

The idea behind the arsenic theory is that arenate, which has 4 O atoms, could provide act as a suitable substrate during Oxygen Evolving Complex to provide the same protons and electron break down.

There is also a parallel chain of thought that arsenic is similar in its makeup to phosphorus, which is needed to create DNA and other genetic material, and so it could help cell division. However, I'm doubtful as arsenic is toxic in any real quantity and thus would be counterproductive to that.