The nervous system of Octopus vulgaris is estimated at around 500 million neurons, comparable in count to a small mammal. The distribution is what makes it strange. Roughly a third sit in the central brain and optic lobes; the remainder are spread through the eight arms, each carrying an axial nerve cord with its own ganglia.
That architecture supports local reflex processing. A severed arm can still perform coordinated withdrawal and reaching movements, and the suckers carry chemoreceptors that let the arm taste what it touches. The central brain appears to issue goal-level instructions rather than specifying every muscle, with the arm sorting out the detail.
This is often reported as the octopus having nine brains, which overstates the case: the arm ganglia are not independent decision-making centres in any ordinary sense, and the central brain integrates vision and learning. What remains genuinely open is how much positional feedback from the arms reaches the brain, since octopuses appear to have limited proprioceptive awareness of their own limb geometry.