An ethical obligation is something that someone is required or compelled to do based on a predetermined set of standards of what is right and wrong. For example, doctors have an ethical obligation to do no harm while diagnosing and treating patients.
Ethical obligations are things a person must or should do based on a code of ethics. Ethics are not inherently based on laws, religion or one's personal feelings, but ethical obligations for professionals, like lawyers and doctors, can be codified into law. For example, according to the Wyoming State Bar, lawyers have an ethical obligation to keep their clients' confidentiality, but there is also a legal requirement in place that makes it absolutely necessary for lawyers to keep confidential information to themselves and to protect that information from becoming public. For some people, perhaps, the ethical obligation would be enough, but the law backs up this ethical obligation as an added measure of security.
Professionals are not the only people who can be bound by ethical obligations. Many people have a strong sense of right and wrong and feel ethically compelled to act when they see something that they feel is wrong or unjust. When a person who is not a police officer or other person who is professionally duty-bound to intervene interrupts a man who is about to strike a child, the intervening person is likely bound by a sense of ethical obligation to help protect a helpless child.