I used to be Roman Catholic, and when I was, I remember the priest sprinkling the people with Holy Water before the beginning of Mass. This is called Asperges. However, I have not yet seen this done at an Orthodox Church (except in the Liturgy itself, on Theophony Sunday) , or an Eastern Catholic one (where one finds holy water fonts). Is the rite of censing the people the equivalent in the East of sprinkling with Holy Water in the West? Or, is the significance different? Also, why is the censing of the people part of the Divine Liturgy whereas Asperges in the West is not considered a part of the Mass proper? Thanks.
Censing and Asperges have different origins and purposes. The Asperges seems to be tied to Epiphany, sanctification of waters and the blessings associated with it - so it's tied to sanctification and purification.
Censing is an extension of burning incense as an offering - an act that clearly predates Christianity. Censing is the burning of incense as an offering, and the offering of prayers. It is done at the points of movement in the services (Entrances in Liturgy, the dance & entrance of the newly baptized and chrismated, the movement of the body in the Funeral, movement of the people & offering at the Blessing of the Loaves, etc.), and at special blessings (other points in the funeral, Trisagion / Memorials, etc.).
The prayer offered for incense at the preparation of the gifts tells much of the story: "We offer to you incense, O Christ our God, as an offering of spiritual fragrance. Accept it now before your heavenly altar and send down upon us in return the grace of the All-Holy Spirit." Then again there is the hymn of vespers: "Let my prayer arise as incense before you..."