The Octave of Prayer for Christian Unity runs from 18 January through 25 January. This coincides with the Week of Prayer for Christian Unity. The former, as Father Phillips points out here, takes a specifically Catholic point of view on Christian unity and has done so since the early 20th century.
From the course on Ecclesiologie et Écumenisme I took years ago at l’Université de Fribourg (Suisse), I vaguely recall that the Catholic Church was a bit slow in coming to the ecumenism table officially. The precise reasons for the delay might or might not be important for us today. But what is important is that the Catholic Church is committed to the realization of our Lord’s prayer that all may be one and that all Christians are reminded, especially during these days in January, to be united in this same prayer.