Updated: Sep 1
Resource guarding is what we call it when a dog worries about people or other animals getting close to his stuff, reaching toward his stuff, or trying to take stuff out of his mouth. (Don't ever do that unless it's a dire emergency! Trade food instead.)
His stuff might be food, a bone, a toy, or just something on the ground. I have even seen a dog who guarded furniture when he wasn't even sitting on it.
Although guarding your valuable items is normal, for dogs and humans, it's a problem when the dog is ready to bite people passing too close. It's a problem if there are young kids in the house, too, as they may reach for an item without understanding. We often exacerbate this problem by taking things away from young puppies or scolding and punishing them for taking things because we aren't teaching the dog not to take things, we are teaching the dog that people take his stuff and that people are threatening and scary when he has stuff in his mouth. More info here and here.
This video gives an excellent overview of the work we do to change the dog's idea about people being near stuff. We also teach a strong "Drop it!" cue. I do not recommend you do this without professional assistance if your dog is growling or biting.
Until you can get help with this work, stop giving your dog bones/toys to guard, keep the house picked up if he steals and guards objects like shoes, dirty laundry, etc..., gate off areas where he jumps up to steal things, and if he guards food only feed him in a confined space. After he leaves that space, move him to another confined space before going to retrieve the bowl. (If he tends to move food out of his bowl, add something wet to prevent that behavior.)
If he manages to get something, do not take it. Instead, make a trail of treats into a room with a door. Close the door behind him after he follows the treats. Remove the item only when he is confined and replace the item with another treat. That isn't training, that's just self-preservation and management.
If he guards the bed or couch when you approach, stop approaching and instead make a game of calling him away to do something fun. Use a cue like "here!" or a hand target. Train him to prefer his own bed to yours, too. We can also work on changing how he feels about being approached so he no longer feels worried.
In all instances, we want to change the emotion driving the behavior, not punish the behavior without addressing the emotion, or we risk making the situation worse or losing the warning signals and creating a dog who goes straight to biting.