When we talk of divine impassibility, we are using negative language. We are saying what God is not. Theologians often have to resort to negative language when describing the being of God. He is impassible, infinite, incomprehensible, immutable and so on. This reminds us that God's being is a great mystery. From our stance as finite human beings it is easier for us to say what he is not than what he is. We should exercise reserve and modesty before the great mystery of God's being. He is above and beyond us in every way.
God's impassibility is a quality of his aseity or divine fullness. Unlike us, God is not dependent upon anything outside himself for emotional fulfilment or satisfaction. I've been dipping into David Bentley Hart's The Beauty of the Infinite. He discusses the divine impassibility or apatheia against the background of the intertrinitarian fellowship of the Father, Son and Holy Spirit in the Godhead.
"I can at least offer a definition of divine apatheia as trinitarian love: God's impassibility is the utter fullness of an infinite dynamism, the absolutely complete and replete generation of the Son and procession of the Spirit from the Father, the infinite "drama" of God's joyous act of self-outpouring - which is his being as God. Within the plenitude of this motion, no contrary motion can fabricate an interval of negation, because it is the infinite possibility of every creaturely motion or act; no pathos is possible for God because pathos is, by definition, a finite instance of change visited upon a passive subject, actualising some potential, whereas God's love is pure positivity and pure activity." (The Beauty of the Infinite: The Aesthetics of Christian Truth, David Bentley Hart, Eerdmans, 2003, p. 167).