The conception of holiness as being a kind of a service to the gods was a common one in ancient Greece, and one of which Plato disapproves. The problem with it is that it implies some sort of dependence of the gods upon us. Socrates' original suggestion, that our relationship with the gods is similar to that between a groom and a horse, suggests that somehow we are the caretakers of the gods--that we improve them, and that they are only made better through our good deeds. If this were true, the gods would be far less omnipotent than we might like to think. The alternative suggestion, that we are the servants of the gods, is also problematic, as it suggests that the gods need us to achieve their goals. Again, this would imply some sort of dependence of the gods upon us, which might undercut their supposed omnipotence. The final alternative is that our service simply pleases the gods without helping them in any way, which would make Euthyphro's task one of identifying why the gods should be pleased by our holy deeds, and what sorts of deeds would please them.
Socrates' demand that Euthyphro identify the one principal goal that the gods use us to achieve is similar to his original demand that Euthyphro identify the one feature that all holy deeds have in common. Though reading a discussion of the Theory of Forms into this dialogue is probably a mistake, we can certainly see the germs of this theory forming in Plato's mind. Throughout the dialogue, there is a sense that we should be able to identify one particular feature that can be said to cover all instances of holiness. If holiness is a service to the gods, then there must be one particular goal above all others which makes the gods want to use us and to reward our holiness.