This section of Barth deals primarily with the knowability of God's Word by humans. That is, can humans know God's Word, and in what sense is this the case?
Barth answers this question in the affirmative. In fact, he states that the knowability of God's word is the "presupposition" of the church. For the church to exist, it is necessary that God's Word has come to humanity. But, Barth is careful here not to classify God's Word as one among many objects of knowledge. Instead, he says, "A result of the uniqueness of this object of knowledge [God's Word] might well be that the concept of its knowledge cannot be definitively measured by the concept of the knowledge of other objects or by a general concept of knowledge but that it can be defined at all only in terms of its own object." (CD I.1. §6.1 p. 190). So, as Barth has previously stated that God's Word is God's speech and God's act, but that it is unlike any other speech and any other act, so too, the knowledge of God's word is possible, but it is unlike any other knowledge known to humans.
The reason this is the case is that God's word is not based upon some "faculty" or "possibility" that is inherent in humanity. Barth will have none of natural theology, none of the modernist or liberal theology that states that in humanity is a special capacity for knowledge of God. No, God's word is not an object of knowledge that is generally available to humans. Thus, the question: if humans have no innate capacity to know God's Word, then how can humans do so? Barth's answer is that the Word of God creates this very capacity of knowledge when it comes. Remember, for Barth, God's word is an event, a specific event, at a specific time, coming to specific men and women ubi et quando visum est Deo (where and when it pleases God). When God chooses to speak, it is always at a specific time and to a specific man or woman, and this very speech of God creates that capacity in those men and women at that time to know, to hear and understand, God's Word.
The consequence of this line of reasoning is that God's word does not linger. Once that specific man or woman has received the gift of the Word of God, it does not pass to them as a possession to be controlled. God's Word remains free to speak when and where God wills. Therefore, the Word of God is always grace, it is always a free gift to a specific man or woman at a specific time.