The original statement of the dilemma is found in Plato's Euthyphro:
Just consider this question:—Is that which is holy loved by the gods because it is holy, or is it holy because it is loved by the gods? (10a)
According to Wikipedia, the question has been reshaped by philosophers and proponents of ethical monotheism to be:
Is what is morally good commanded by God because it is morally good, or is it morally good because it is commanded by God?
But I don't see why the question couldn't be generalized to:
Is what is morally good required by our ethical code because it is morally good, or is it morally good because it is required by our ethical code?
Of course for many codes the answer will be, it's not morally good at all. But all of us hold ourselves (and, very likely, others as well) to some sort of ethical code and to the extent that we do what our code requires, we feel justified in calling our actions good. Is there some greater, abstract, ideal of good that is reflected in our ethical codes or do our codes themselves define the good?
Many of the traditional solutions to the dilemma turn on some conception of a monotheistic God. I'm not sure how many, if any, will work for secular ethics.
While it might be tempting to simply say that ethical codes define goodness, we are then forced to ask the meta-question:
How can we choose one ethical code over another?
Whatever criteria we pick will then, itself, be subject to the Euthyphro dilemma.
Socrates and Euthyphro do not themselves resolve the dilemma. Plato, however, does assert the Form of the Good in other writings, which suggests that he would say our moral codes merely reflect goodness and are not themselves a complete picture of the Good.