One notices PD symptoms usually on one side of the body, this is called "hemiparkinsonism", where "hemi" means "half".
It is this way because the brain is naturally divided into two "hemispheres" the left side of the brain controlls the right side of the body and the right side of the brain controlls the left side of the body.
Just like we have two eyes, the structures in the brain that die off are two pea size peices of tissue that compose the "substantia nigra". Usually, for reasons unknown , the dopaminergic cells in one of the pea like structures in one of the brain hemispheres die off at a greater rate than in the other half of the brain. Eventually, we lose a critical amount of cells in the other half too, and this is known as becoming "global". This means that both sides of the body suffer PD symptoms.