1st definition:
Piety =df what Euthyphro is doing, namely, prosecuting his father.
Fails because:
it does not show why other pious acts are pious (indeed, it does not show why Euthyphro's own act is pious).
2nd definition:
Piety =df what the gods love.
Fails because:
(a) Euthyphro holds that the gods differ about what they love and
(b) a single action cannot be both pious and not pious.
3rd definition:
Piety =df what all the gods love (Compare: the right, the good is what God loves or approves of.)
Fails because:
(a) the reason for applying a descriptive label is not the same as a reason motivating a particular action (although each may be indicated by the word "because").
(b) "what all the gods love" is a descriptive label applied correctly just in case it matches the facts, which in this case would be something being loved by all the gods
(c) the motivating reason for all the gods loving some X (and all actions including loving have a motivating reason) is, Euthyphro asserts (pushed by Socrates), that X is pious (a descriptive label). But then:
(d) the motivating reason for the gods' love presupposes the truth of the descriptive label, to wit, that X is pious, and independently of being loved by all the gods (otherwise, there could be no motivating reason).
Piety is, then, loved by the gods because it is pious,
though something may be said to be in a state of being loved by the
gods simply in virtue of their loving it.