Homily

A homily is a commentary that follows a reading of scripture. In Catholic, Anglican, Lutheran, and Eastern Orthodox Churches, a homily is usually given during Mass (Divine Liturgy for Orthodox and Eastern Catholic Churches, and Divine Service for the Lutheran Church) at the end of the Liturgy of the Word. Many people consider it synonymous with a sermon.

According to The Catholic Encyclopedia:

The word homily is derived from the Greek word ὁμιλία homilia (from ὁμιλεῖν homilein), which means to have communion or hold verbal intercourse with a person. In this sense homilia is used in 1 Corinthians 15:33. In Luke 24:14, we find the word homiloun, and in Acts 24:26, homilei, both used in the sense of "speaking with". Origen was the first to distinguish between logos (sermo) and homilia (tractatus). Since Origen's time homily has meant, and still means, a commentary, without formal introduction, division, or conclusion, on some part of Sacred Scripture, the aim being to explain the literal, and evolve the spiritual, meaning of the Sacred Text. The latter, as a rule, is the more important; but if, as in the case of Origen, more attention be paid to the former, the homily will be called expository rather than moral or hortatory. It is the oldest form of Christian preaching.

The General Instruction of the Roman Missal (GIRM)

29. When the Sacred Scriptures are read in the Church, God himself speaks to his people, and Christ, present in his own word, proclaims the Gospel. Therefore, all must listen with reverence to the readings from God's word, for they make up an element of greatest importance in the Liturgy. Although in the readings from Sacred Scripture God's word is addressed to all people of every era and is understandable to them, nevertheless, a fuller understanding and a greater effectiveness of the word is fostered by a living commentary on the word, that is, the Homily, as part of the liturgical action.

...
Wikipedia