A dog nudging its food with its nose might be because the food isn't tasty, and the owner can try replacing it with something more appealing. Some clever dogs nudging food with their noses are reminding their owners to save any uneaten food. Dogs have a habit of hoarding food, and nudging food with their noses could also be a way of trying to hide it.
Why dogs root for food
When a dog doesn't like a particular food, it will nudge it with its nose, trying to pick out the best parts. If the owner then offers a different, more palatable food, the dog will stop nudging it when it eats it.
Some dogs are quite clever; when they can't finish their food, they'll nudge it with their noses to remind their owners to put the food away and offer it to them again next time.
Dogs using their noses to root at food may also be related to their habit of hiding food. Some dogs will dig a hole in the ground, root the food in, bury it, and then dig it out to eat when needed.