It may be that we can see, with the advantage of insight or psychological analysis (Freud is read these days as much by literary critics as by psychologists), that he or she was internally or externally influence without realizing it, so that the poem points in directions which have only subsequently become clear, and perhaps could not have been imagined by the writer.
We may actually know more about the author than was, and that could have been, present to his or her mind at the time.
This is true, but N.T. Wright goes out of his way earlier to play down this sort of interpretation. It has value but is easily overused and can quickly break down into conjecture. C.S. Lewis absolutely hated this sort of thing and would only admit it had any value at all if pressed hard.
This whole idea of the writer putting things down that have more meaning than even he realizes though is all tied up with the idea of the divine inspiration of scripture. Wright continues:
..there is an analogy between this level of inquiry and the suggestion, sometimes made within more traditional biblical exegesis, that there exists, over and above the author’s meaning, a sensus plenior, by which an ‘inspired’ text actually says MORE than the author realized at the time, with the Holy Spirit filling in the blank of authorial ignorance, or bringing about an ‘unintended’ prophecy by which (for instance) Caiaphas speaks a word of the Lord even when intending to say something else.
The recognition of such a sense, and the possibilities for allegorical and other exegesis which it opens up, have at various stages of the church’s reading of scripture been ways of allowing for the experience of Christians that the biblical text ‘speaks’ to them in ways that the author might not have imagined.
-N.T. Wright, The New Testament and the People of God, p.56