An ethical or moral dilemma is a situation in which a person is required by their ethical code to take at least two actions and, while able to take either, is not able to take both. In other words, they face an ethical failure no matter how they choose to act.
There are examples of ethical dilemmas from a range of settings, from business to parenting and healthcare to warfare.
Perhaps the most famous ethical dilemma in philosophy was posed by Socrates in Plato's Republic. In response to an assertion by Cephalus that justice consists of speaking the truth and repaying debts, Socrates points out that repaying a debt of a borrowed weapon to a friend who might hurt someone with it would represent a failure in justice. Therefore one must choose between repaying a debt or protecting others from harm, both of which are mandated by one's ethical code.