The O Antiphons refer to the seven antiphons that are recited (or chanted) during Vespers of the Liturgy of the Hours. They cover the special period of Advent preparation known as the Octave before Christmas, Dec. 17-23, with Dec. 24 being Christmas Eve and Vespers for that evening being for the Christmas Vigil.
The importance of O Antiphons is twofold: Each one highlights a title for the Messiah: O Sapientia (O Wisdom), O Adonai (O Lord), O Radix Jesse (O Root of Jesse), O Clavis David (O Key of David), O Oriens (O Rising Sun), O Rex Gentium (O King of the Nations), and O Emmanuel. Also, each one refers to the prophecy of Isaiah of the coming of the Messiah.
First some definitions:
Antiphon: A short verse from a psalm or other, usually biblical, source, sung or recited before or after a psalm or between verses. (The most familiar example is probably the responsorial psalm that is part of each Mass.)
Liturgy of the Hours: The official cycle of the Church’s daily prayer, also known as the Divine Office. It consists of hymns, antiphons, psalms, selections from Sacred Scripture, readings from the Church Fathers, commentaries on the Scriptures and the Christian life, writings of the saints, and standard Catholic prayers. Priests and religious are obligated to observe this cycle of prayer, and all the faithful are invited to join. It can be prayed publicly or privately. You can find information and the prayers online here. Click on General Instructions or Breviary Bootcamp to get started.
Vespers: The evening service of the Divine Office, also known as Evening Prayer.
Octave: Latin for eight. The practice of celebrating a major feast on the day itself and then for seven days following. In this usage, it is an octave of preparation for the great celebration of the Nativity of Christ!
O Sapientia: O Wisdom, O holy Word of God, you govern all creation with your strong yet tender care. Come and show your people the way to salvation. Isaiah had prophesied, The spirit of the Lord shall rest upon him: a spirit of wisdom and of understanding, a spirit of counsel and of strength, a spirit of knowledge and fear of the Lord, and his delight shall be the fear of the Lord. (11:2-3), and Wonderful is His counsel and great is His wisdom. (28:29).