Is a priest's sermon an explanation of bible? When a priest reads a gospel in mass he ends saying, "the gospel of the 
Lord", then continues and says today's gospel is about, does this mean that the priest is explaining that part of the bible? Or in other words, the gospel is part of the Bible, and the priest is explaining it?
The Short Answer

In the homily the priest proclaims the mysteries of the faith and the standards of the Christian life by way of the scripture readings and the liturgical prayers.  He does this in a way that nourishes the Christian life of the listener.

Part of the priest's job in the homily is to explain the Bible, but he is supposed to be doing more than that.  The homily is an organic part of the liturgy, not some separate, detached sermon.  So the priest is interpreting the Bible in light of the liturgy, the mysteries of the faith, Christian living, and the particular lives of his congregation (cf. Homiletic Directory, 16).  Some days the priest may focus very heavily on the scripture readings.  Other days he may just touch on them while focusing on other matters.

At the end of the day the priest preaches to try to bring you closer to Jesus Christ.  Explaining the scriptures is a central part of that and an essential means, but it is not the only part.

The Long Answer

Here are some quotes from Catholic documents on the topic:


  [The homily] should be an exposition of some aspect of the readings from Sacred Scripture or of another text from the Ordinary or from the Proper of the Mass of the day and should take into account both the mystery being celebrated and the particular needs of the listeners (General Instruction of the Roman Missal, 65).





  Through the course of the liturgical year the homily sets forth the
  mysteries of faith and the standards of the Christian life on the
  basis of the sacred text. [...] The purpose of the homily at Mass is
  that the spoken word of God and the liturgy of the Eucharist may
  together become "a proclamation of God’s wonderful works in the
  history of salvation, the mystery of Christ" [SC 35, 2] (Introduction of the Lectionary for Mass, 24).


(Note here that the words 'sacred text' "refer to the biblical passages and the prayers used in a liturgical celebration" [Homiletic Directory, 11].)




  Whether the homily explains the text of the Sacred Scriptures
  proclaimed in the readings or some other text of the Liturgy, it must
  always lead the community of the faithful to celebrate the Eucharist
  actively, "so that they may hold fast in their lives to what they have
  grasped by faith" [SC 10] (Introduction of the Lectionary for Mass, 24).





  In sum, the homily is shaped by a very simple dynamic: it reflects on
  the meaning of the readings and prayers of a given celebration in
  light of the Paschal Mystery; and it leads the assembly to the
  Eucharistic celebration in which they have communion in the Paschal
  Mystery itself (Homiletic Directory, 15).





  Looking at this fundamental pattern of preaching in the Emmaus
  narrative illustrates the essential connection between Scripture, the
  homily, and the Eucharist; for it was in the “breaking of the bread”
  that the disciples ultimately recognized their Risen Lord, and it was
  then they realized that their hearts were burning within them “while
  he spoke to us on the way and opened the Scriptures to us” (Lk 24:32).
  This is why virtually every homily preached during the liturgy should
  make some connection between the Scriptures just heard and the
  Eucharist about to be celebrated (Preaching the Mystery of Faith: The Sunday Homily, pg. 20).





  The full scope of Jesus’ preaching reminds us that when we have the
  privilege of preaching the homily to a congregation at the Sunday
  Eucharist, we also have an invaluable opportunity to advance the
  Church’s catechetical ministry.38 This intrinsic relationship between
  preaching, doctrine, and catechesis is also reflected in the ministry
  of Paul the Apostle (Preaching the Mystery of Faith: The Sunday
  Homily, pg. 21).