In reply to Leeneia's query about the liturgical function of the O Antiphons, they are sung with the "Magnificat" (or "Song of Mary" from the first chapter of Luke's Gospel) at Vespers (Evening Prayer) on the days leading up to Christmas -- so not at the Mass (though some parish churches may use "O Come, O Come, Emmanuel" at Mass as a congregational hymn). The Magnificat is sung at Vespers every day of the year, but the antiphon that is sung with it varies according to the day of the week, the season of the year, or the particular feast that occurs on a given day.

Oddly enough, antiphons aren't technically "responses". In the early church, there evolved two distinct ways of singing psalms and "canticles" (like the Magnificat): "antiphonally" and "responsorially". Just what these terms meant in Late Antiquity is actually very difficult to recover. It seems that antiphonal singing involved (as in later definitions) alternation between two choirs facing each other, but also the use of a chant called an "antiphon" that functioned as a refrain that was passed somehow between the two sides. Responsorial singing, by contrast, involved the singing of a psalm by a soloist, with the congregation or choir inserting a refrain ("responsory" or "respond") after each verse or after groups of verses. Eventually, antiphonal singing and responsorial singing became virtually indistinguishable in liturgical contexts: both antiphons and responsories are really just refrains sung by the congregation/choir. As a rule, antiphons tend to be fairly simple and responsories tend to be rather more complex (compare the "Introit antiphon" and the "Gradual responsory" in the Gregorian chants that accompany a Roman Catholic Mass), though there are of course exceptions ("Offertory antiphons" are notoriously tricky). And there are blurred boundaries in some historical sources: I've found an eighth-century Anglo-Saxon description of antiphonal singing in which the psalm is sung by a soloist and a chant called an "antiphon" is passed from side to side by two choirs after every verse.

In modern practice, an antiphon is sung before and after a psalm (or, as with the Magnificat, a canticle), and the melody of the antiphon determines the recitation tone to which the psalm itself will be sung.

The Introit antiphon at a Mass is somewhat different: originally it would seem that a whole psalm was sung, but this was eventually (by the ninth century) truncated to a single verse. The Introit antiphon is repeated several times: Antiphon - Verse - Antiphon - Doxology ("Gloria Patri...") - Antiphon.

I hope this is helpful. Good luck as you persevere with the arcane terminology of Christian liturgy!

Jesse