In the Roman Rite, when a higher-ranked liturgical celebration impedes the celebration of a lesser one that, either permanently or (in a particular year) by coincidence, falls on the same day, the prayer of the lower-ranked celebration is usually added to that of the higher. This additional prayer is referred to as a commemoration of the lesser celebration.
In the post-Tridentine usage, on Sundays lacking the commemoration of a feast of Double rank, or of an Octave, a second and a third prayer was added to that of the Sunday. These were called "seasonal" (in Latin, pro diversitate temporum) prayers, not "commemorations". For instance, from Advent to 2 February, the first of these additional prayers was in honour of Saint Mary and the other was either that "Against the persecutors of the Church" or that "For the Pope".
At Mass, commemorations were made by adding the Collect, Secret, and Postcommunion of the commemorated celebration after the ones for the higher-ranking celebration. If three or more commemorations were made, the conclusion ("Per Dominum..." or its variants) was omitted in all but the first and last. In the Office, commemorations were made only at Vespers and Lauds, using the Antiphon on the Magnificat or Benedictus, the Versicle and Response normally following the hymn, and the collect, all said after the collect of the current day. Also at Matins, the ninth Lesson was usually read of the commemorated day, except on Sundays and on certain high-ranking feasts.
The 1970 Mass of Paul VI eliminated commemorations, laying down that only one prayer should be used, admitting some flexibility in the choice of the prayer. The new Missal uses "Memorials", celebrations of saints at a level lower than that of Feast or Solemnity, which are not to be confused with commemorations.