Duty of care means someone does not owe you a reasonable standard of care unless there is a duty of some sorts between you. According to FindLaw, that duty arises simply when an individual in some way, shape or form interacts with you. It could be you went around them, you drove around them, you sold them a product or something like that. But in some way, shape or form, you are interacting with that individual. And when you do, you owe a reasonable standard of care to that individual. That is, you have to use reasonable care and skill in avoiding causing injury to that person.
In some cases, even non-action can give rise to liability for failure to make a standard of care. The general rule is if you do not have any duty to someone, then you do not owe them a standard of care. So non-activity is not actionable. If you are walking by a lake and you see someone drowning, are you potentially liable for not helping them? You can watch them drown, and you will not be liable. But that changes if for some reason you have a special relationship with that person. It could be your brother, parents, child or anyone like that. Because of your unique link, you could have a duty there and could be liable if you do not help them.
By interacting with individuals, you incur some duty or standard of care with them. In some cases where you are not directly interacting with them, but you have a special relationship or you undertake to help them, you could incur that obligation or duty of care.