Training is also beneficial for your dogs' health as it provides mental stimulation for them and sets the order of dominance in their pack (you, your family and your dog).
Dogs are a pack animal and need this order to be well establish to feel safe and secure. It is also important that your dog understands that you are the top dog. If your dog thinks that they are top dog this can lead to a lot of problems, particularly if you have children in your family.
Training particularly with a qualified trainer can teach both you and your dog how to set these rules in place and help to provide a happy and secure environment for both you and your dog.
It is also important to remember that you are only able to have your dog off-leash in off-leash areas if the dog is under effective voice control. This is for your dogs safety as well as for others using the area.