Mothers' breasts are sometimes so full that they must offer them to some child, and though the child takes the breast with great avidity, the nurse offers it still more eagerly, the child pressed by its necessity, and the mother by her abundance.St. Francis of Sales. Treatise on the Love of God (Chapter XV, "Of the affinity there is between God and man"). Kindle Edition.
The context is the divine eagerness to communicate Its goodness to mankind, and the poverty of man who needs God's grace. This is the affinity between man and God, writes this saintly doctor of the Church -- the one with a void that the other is only too eager to fill. Like a mother breast feeding her child.