What does it mean that God "changes his mind" (Ex.32:12)?

Yet, we still have to discover what God "changing his mind" might mean?  Again, it is Frethiem who offers wise insight here so I will quote him at some length. 

"What status do (Moses') arguments have for God?  They are certainly not matters that God had not considered before.  But to have them articulated in a forceful way by God's own chosen leader gives them a new status.  Moses, by his entry into the discussion, brings three new factors to bear on the situation:  his decision or will, his energy (!), and his insight.  These factors make the situation different from what it had been moments earlier.  God is open to what Moses has to say and takes Moses' contribution with utmost seriousness, honoring it as an important contribution for the shaping of the future.  If Moses wills and thinks and does these things, they take on a significance that they did not carry when  treated in divine isolation.  It is not a matter of Moses winning the argument but of a relationship that God takes seriously. . . 

"The God of Israel is revealed as one who is open to change.  God will move from decisions made, from courses charted, in view of an ongoing interaction with those affected.  God treats the relationship with the people with an integrity that is responsive to what they have to say.  Hence, human prayer (in this case intercession) is honored by God as a contribution to a conversation that has the capacity to change future directions for God, people, and world.  God may well adjust modes and directions (though not ultimate goals) in view of such human responsiveness.  This means there is genuine openness to the future on God's part, fundamentally in order that God's salvific will  for all might be realized as fully as possible.  It is this openness to change that reveals what it is about God that is unchangeable:  God's steadfastness has to do with God's love; God's faithfulness has to do with God's promises; God's will is for the salvation of all.  God will always act, even make changes, in order to be true to these unchangeable ways and to accomplish these unchangeable goals" (Exodus, 5161). 

Friends, these are among the most important words ever written about a passage of scripture, in my judgment.  Not only does it tell us something incredible about our God, something often hidden from us by our theology or unwillingness to believe God could really be like that, but something nearly unbelievable about ourselves.  We are meant for such a relationship with the Lord God Almighty, YHWH, the God and Father of our Lord Jesus Christ!  It's all by grace, of course, but we seldom hear such intimacy, boldness, and importance to God are ours in Christ.  That we truly do have God's ear, that what we have to say matters to him and might even play a role in God "changing his mind" and thus shaping the future of our lives and world . . . you tell me, have you ever heard that before?  The astonishing reality of this relationship also puts in sober relief the deep tragedy of turning away from God and the remarkable stakes that are on the line in such apostasy and idolatry.