Genuflecting (bending the knee) or bowing / bending one’s head are both gestures of respect. Both were once common in civil society as gestures or respect for high officials, royalty, etc. but are now most often seen in the context of worship.
In the Letter to the Philippians chapter 2, verse 10, Paul writes “at the name of Jesus every knee should bend”. Genuflection (sometimes spelled genuflexion) is an action which involves “touching a knee briefly to the floor while holding the upper body upright, and then returning to a standing position. It is not required by the Prayer Book at any time. In some parishes it is a customary gesture of reverence for Christ’s real presence in the consecrated eucharistic elements of bread and wine. Genuflections are often customary in parishes with an Anglo-Catholic piety. Genuflections may be seen as people enter or leave a church”. 
Today, a “profound bow of the head and upper body is now more frequently used … not least because it is a more graceful action and less awkward to perform”. 
Both gestures are examples of “body language”. Archdeacon Ian Stuchbery describes bowing, genuflecting and making the sign of the cross as examples of body language and goes on to say:
“There are means of communicating other than with the voice. A kiss, a handshake, a smile are all ways in which we ‘talk’ to one another without speaking. Religion also has sign language which is used in worship and in our private devotions. Bowing (the slight inclination of the head and shoulders) is a gesture of recognition, devotion, or thanks. In church one bows when moving in front of an altar (the symbol of God’s presence) and at certain points in the liturgy, for example, at the name of Jesus. This is simply a physical way of acknowledging God and expressing our feelings of devotion before him. In a similar way, the ancients would ‘fall on their faces’ in the presence of the holiness of God. Bowing is a simple way of saying ‘thank you’ when the ministers at the altar assist one another in the conduct of the Eucharist. It saves speaking, and so is not distracting to others”. 
As with many other customs and traditions, the practice of genuflecting or bowing is a personal choice in the Anglican tradition. It is considered an adjunct to worship and prayer but not a requirement.
 “Genuflection, or Genuflexion” in: An Episcopal Dictionary of the Church: A User-Friendly Reference for Episcopalians. Edited by Don S. Armentrout and Robert Boak Slocum. New York: Church Publishing, 1999. “Gestures. 7. Bending the Knee and Bowing the Head” in: The New Westminster Dictionary of Liturgy and Worship. Edited by Paul Bradshaw. Louisville: Westminster John Knox, 2002.  “Bowing, Genuflecting, and Crossing” in: This Is Our Faith: a Guide to Life and Belief for Anglicans with a Revised Chapter on Worship / Ian Stuchbery. Toronto: Anglican Book Centre, 1990, p. .