ased muscle activation - thicker handles stimulate much more muscle activation in the hands and forearms and in the upper arms and whole upper body. More muscle activation means much bigger muscle and strength gains.
"Unlocking" muscle gains - thick bars make your hands, fingers and forearms so much stronger that your body can finally stop "holding back" the strength and muscle gains in your uppers arms, back and chest.
Complete training - thick bar training automatically trains your hands, fingers and forearms at all angles. If you are bench pressing, the thick bar will train your hands and forearms in a completely different way than if you are doing chin ups on a thick bar.
Natural movement - thick bars perfectly replicate the natural function of the human hand - lifting heavy, awkward objects.
Automatic training - thick bars means you are training your grip the whole time and you don't even need to do any extra exercises.
Concentration - thick bars are harder to handle so you need to concentrate a lot harder to lift the weight. Some credit this alone with making them significantly stronger.
Less imbalances and injuries - thick bars shift the stress off the joints and onto the muscles because a thick bar spreads the weight over a larger area.