Simply put that a hunter's pet is something like your friend on the battlefield. They will fight with you, their purpose is to hold aggro and let you shoot from distance safely.

You must keep your pet happy at all times or it'll leave you or even turn on you. You can see your pet's hapiness level at their icon.

Pet fights more = become unhappy
Feed them food = become happy

When their happiness drop, their attack damage will also drop. Pets at full happiness(green smiley) will do 125% damage. Pets at average happiness(yellow smiley) will do 100% damage. Unhappy pets will do 75% damage. So you have to keep your pet happy at all times to get max damage from your pet.

^^ what he said!