To make it plain and simple, Aristotle's "golden mean" is that we should have moderation in everything. Too much of anything can be bad. The Complete Idiot's Guide to Philosophy defines the golden mean this way: "A mean is a middle way or a medium degree. The golden mean is a rule that says you shouldn't do anything to excess."
Medea violates this rule of moderation in two ways: her excessive love for Jason and the extreme way she seeks revenge on his infidelity.
In lines 110-14, Medea rages and screams at her children:
I am in agony, I am so brutally misused.
You horrible children, of a mother who hates you
god damn you with your father,
and the whole house go to Hell.
The Nurse scolds her and tells her that the children are innocent. She should not hate them. Medea should not let her anger and jealousy get the best of her. In lines 124-30, the Nurse reminds her of the golden mean:
The golden mean, first just to say
its name should win a prize, to apply it
is by far the greatest achievement. But excess
never should have a place in our lives.
It brings all the greater ruin
when some god feels spite toward a house.
Sadly, Medea won't take the Nurse's advice.