This is a representation of what Christians call the Trinity or Triune God--Father, Son, and Holy Spirit. The concept is one of three persons in one God, so that they cannot be separated.
The lamb is the Lamb of God, Jesus, who takes away the sins of the world--a living sacrifice that replaces the animal sacrifices used by the Hebrews to atone for their sins as described in the old testament scriptures. The staff/flag stands for the idea that Jesus is the living Word of God. "The Word was made flesh and dwelt among us, and we beheld his glory, the glory of the only begotten Son of God, full of grace and truth." In the book of Revelation, which is apocalyptic in nature, the imagery used for Jesus is also of a lamb, the lamb who was slain and who is the only one worthy of opening a scroll sealed with seven seals (prophecy).
The dove is a representation of the Holy Spirit as He appeared when Jesus was baptized and is also referred to as the dove of peace (the reason the dove is sometimes depicted with an olive branch) throughout the new testament scriptures, which talk about the Holy Spirit as the comforter and the one who brings faith and peace to all believers. This is also a reference back to the old testament scriptures when God sent a dove with an olive branch to Noah in the ark to let him know that the flood waters were receding, the wrath of God was past, and that he could leave the ark.
The Alpha and Omega represents the idea that the Trinity is one God that has existed since the beginning and will continue to exist throughout eternity. Christians believe that references to the Trinity can be seen in both the old and new testament scriptures, and that the new testament scriptures regarding the coming of Christ are a fulfillment of old testament prophecy. In the beginning of book of Revelation, God claims this identity for himself when he says, "I am the Alpha and the Omega, who is, and who was, and who is to come, the Almighty," and again at the end of the book, when he says, " I am the Alpha and the Omega, the First and the Last, the Beginning and the End." The reason that Greek is used is that the book of Revelation was written by one of the apostles to 7 churches in what was then known as Asia Minor. Greek was the predominant language of the time/area and those receiving the letter (prophecy) of the book of Revelation would have understood the Greek concept of Alpha and Omega as it was being applied to God.