"Often this One who is coming has been presented in formulas that, while true, are nevertheless at the same time outmoded. [...] We must therefore try in fact to express the substance as such - but to say it in a new way." (Kindle locations 931-935)
What sort of thing do you think he has in mind?
Archbishop Chaput , in his book, talks about the address John XXIII gave at the opening of VCII. He said the focus of the council was Aggiornamento and Resourcement. Or, translated: Bringing to date and a return to original sources. I think this plays a lot into what B16 is saying.
He is talking in response to the question shouldn't the Church be speaking in terms of not only where Christ has come but is coming again. The message of the Gospel is eternal and true, but it is not always phrased in a way that can be understood as relevant to the time at hand. It is the job of the Church to safeguard Truth and present it in a relevant way to the people (constantly evangelizing) in a way that is effective but consistent with the Truth and not bowing to Modernism.
This covers all things touched by the Gospel since we can look at the Gospel and sum up much by saying: Christ has died, Christ has risen, Christ will come again.
This most obviously impacts how the Gospel is applied in Truth to social issues of the day while remaining consistent with the Truth.
I'll add examples. Gotta get ready for work.
Adding.
Examples, I think, would involve the interplay between Dogmatic and Moral theology. What I mean by that is we have the Eternal Truths expressed in Dogma as given in Scripture and Tradition and safeguarded by the Church. Then we have Moral Theology, which deals with how to live those truths in an authentic and faithful manner. The Church, as mother and teacher, guides in all of this. So the Church cries out always: "Prepare the way of the Lord." And as pilgrims on earth journeying to our home in the Kingdom of God we need a moral life to ready our hearts. So the Church proclaims the endlessly true Dogmas that involve things like dignity of all life. But we call back with questions. We ask: How do I do this? How do I respect life in a world that disrespects it? How do I achieve faithfulness in a world of transient values? And the Church teaches us.
But in today world, as in every time, there are specific challenges to that living of the Gospel. And it is in that the Church needs to, as B16 says: "say it in a new way"
Not in a changeable way, but an example is what is the place of dignity in an internet age with those ramifications? The core is the same as day one, but the expression to stay faithful to the core is a different mode at some points. That is what he means by outmoded.
So how does the Church guide in preparing our hearts for God though a moral life faithful to the unchanged Truth given the realities of the age. What are the practical modes the message must be in to contain the same Truth but to open our hearts and guide them in present realities.
It is the great fight against modernism, that wants to change the truth to fit the needs of the time. The Church answers that by showing the constant validity of the unchanging Truths She holds as protector. Where the wold says that the Truth is outdated and obsolete, the Church responds by saying: No, here is that Truth and how to live it faithful to the substance of it in this age.
To me the Truths of human dignity are the ones that are in constant need of that living connection to the living Truth of the Gospel because the changes of the age always bring new challenges and questions.