A full image similar to your diagram with chemical reactions is found at a blog Chemistry Tutoring:
According to the UC Davis ChemWiki page Electrochemistry 7: Electrochemical Corrosion, the oxidation and reduction reactions occur in separate places in the metal - in the case of your diagram:
- Oxidation occurs in the anode part of the iron pole submerged in water:
$$\ce{Fe_{(s)}->Fe^{2+}_{(aq)} +2e-}$$
As Burak Ulgat correctly noted in his comment, the $\ce{Fe^{2+}_{(aq)}}$ ions are dissolved in the water and are outside of the pole and are transported by the water. The electrons move through the metal in the pole (as iron is a metal, these electrons conduct easily) - this part is not shown in your diagram.
At the anodic region, for whatever reason, the iron is exposed to the seawater, may already have damage etc, so comes under 'attack'. As $\ce{Fe^{2+}_{(aq)}}$ ions are 'liberated', pitting occurs as material is removed (dissolved) from this area of the pole. Often, these pits are deprived of oxygen, increasing the rate of pitting. The presence of seawater speeds up this process.
- Reduction occurs at the cathode region, oxygen from the air is reduced to form hydroxide:
$$\ce{O2_{(g)} + H2O_{(l)} + 4e^{-}->4OH^{-}}$$
Then rust formation occurs as per the diagram above (summarised below):
$$\ce{Fe^{2+}_{(aq)} + 2OH^{-}_{(aq)}->Fe(OH)2_{(s)}}$$
$$\ce{4Fe(OH)2_{(s)} + O2_{(g)} + H2O_{(l)} ->Fe(OH)3_{(s)}}$$
According to the UC Davis ChemWiki, the process of corrosion continues if the presence of a depolarizer, which removes electrons from the metal, depolarizers include more noble metals, acids and in the case relevant to the diagram, oxygen. So, the oxygen depolarizer is removing electrons out of the iron, resulting in more iron ions being dissolved into the water at the anode.
The electrochemical process is summarised by the HyperPhysics page about Corrosion as an Electrochemical Process, in the diagram below:
