Barth’s clarity is not something for which he is particularly known, but I think these comments from Joseph Mangina, in Karl Barth: Theologian of Christian Witness, make sense of the sort of clarity Barth sought:
While acquaintance with the structure of the Dogmatics is useful, it does not prepare one for the actual experience of reading the text. A main reason is that Barth does not adopt the familiar persona of the impartial academic. He writes not impartially, but as a partisan; he writes as one who is passionately engaged in the very subject matter under discussion. Barth seeks to foster this kind of engagement in the reader as well. He draws the reader into a movement of reflection, examining a theological puzzle from different angles, at times leading him or her down false roads (only so will we understand why they are false), always pressing us forward to some resolution of the problem at hand. Barth will never say in the manner of textbooks: ‘Here are two ways of looking at the topic, take your choice.’ The nature of what the church proclaims demands clarity. If anything frustrates him in modern theology, it is the tendency one sometimes sees to celebrate doubt and ambiguity for their own sake. Barth believes the Word of God to be an ultimate mystery, but he does not see it as opaque. Because God has spoken clearly in Jesus Christ, we can actually arrive at answers to theological questions. To be sure, our answers — being human — are always contestable; but the best way to see where we have gone wrong is to express our thinking as clearly as possible. This is a key reason why Barth wants to embrace the modern term wissenschaftlich, ‘scientific’, for Christian theology. All this makes for the curious blend of passion and objectivity one finds in his writing. As Hans Urs von Balthasar writes, Barth is ‘passionately enthusiastic about the subject matter of theology, but he is impartial in the way he approaches so volatile a subject. Impartiality means being plunged into the object … And Barth’s object is God, as he has revealed himself in Jesus Christ, to which revelation Scripture bears witness’ (The Theology of Karl Barth, Ignatius, p. 25).