It reminds the Church founded by the resurrection that as such it stands under the Cross, which means, in the concealment of God which He Himself alone breaks through when it pleases Him. It reminds it that the relationship of head and body is not reversible, that the healing omnipotence is the power of the Lord: it is over us and for us without ever becoming our power.
It is one of my general contentions in interpretation that every metaphor breaks down somewhere, and nowhere is this more true than metaphors about man's relation to God. The place where I discovered this is the beginning of Jeremiah, where Israel is compared to, variously, a wife, a child, and many other things besides. Each picks up a particular aspect of what it means to relate to God, but none of them expresses it fully--and terrible misinterpretations happen when one metaphor is privileged, or extended too far. Barth here, by reading the metaphor of head and body, shows the definite limits of another metaphor--bride and groom. The church is, in some sense, the bride; marriage is a picture of at least one aspect of the relationship between Christ and the church (certainly one that speaks of love; perhaps, though not certainly, other things as well). On another level, though, the metaphor is wrong, because marriage is a relation between two equals (or, for the complementarians out there, separate-but-equals), which the relationship between Christ and the church never can be. The church is made of men, who fail, and only after very much trouble throughout their lives can approach even a portion of what God has (or can only do so through God's grace--but no one would say this about a husband's relationship to his wife); Christ, especially the ascended, glorified Christ, does not have any of these weaknesses or failings. And, indeed, the church is one of the things that will pass away--the church only becomes possible after the ascension, and will be rendered meaningless after the return (they will neither marry nor be given in marriage, after all). We are, in this sense, and as Kierkegaard said, living in the parentheses. Placing the ascension, along with the incarnation and the sepultus, as the key moments in the Creed and the Bible permit a full, proper conception of the relationship between God and man.