The Entrance Antiphon, taken from the Common of Several Martyrs for Eastertide, was given as being Rev. 7:13-14:
These who are clothed in the white robes are they who have survived the time of great distress and have washed their robes in the blood of the Lamb, alleluia.The Scriptural reference is clearly to times of persecution and martyrdom, and the word distress used in the antiphon might more usually be recognised as being translated as persecution.
The prayer said by the priest at Mass immediately after the Our Father also includes the word distress, that word in the new translation replacing the word anxiety in the previous translation:
Deliver us, Lord we pray, from every evilThe resource Become One Body One Spirit in Christ points out that the last two lines of this prayer are a quotation from St Paul's letter to Titus (Titus 2:13), and only comments generally on a wider sense that the word distress has compared to the previously used word anxiety.
graciously grant peace in our days,
that, by the help of your mercy,
we may be always free from sin
and safe from all distress,
as we await the blessed hope
and the coming of our Saviour Jesus, Christ.
I have not been able to verify textually whether or not the use of the word distress in this prayer of the Communion Rite at Mass is a really intended reference to martyrdom (and therefore the intercession for "peace in our days" a specific prayer that the Church might live in peace and not just a prayer for peace in general). It might just be an accident of translation. The more knowledgeable might like to enlighten me via the comments box.
But if we grant that it is a reference to martrydom, its location in the Communion Rite where we approach a most intimate moment of union with God and our fellow believers is interesting. The following passage from the encyclical Ut Unum Sint n.84 offers an insight into the relation of distress to communion:
In a theocentric vision, we Christians already have a common Martyrology. This also includes the martyrs of our own century, more numerous than one might think, and it shows how, at a profound level, God preserves communion among the baptized in the supreme demand of faith, manifested in the sacrifice of life itself. The fact that one can die for the faith shows that other demands of the faith can also be met. I have already remarked, and with deep joy, how an imperfect but real communion is preserved and is growing at many levels of ecclesial life. I now add that this communion is already perfect in what we all consider the highest point of the life of grace, martyria unto death, the truest communion possible with Christ who shed his Blood, and by that sacrifice brings near those who once were far off (cf. Eph 2:13).