"Antiphon" - a piece of music where alternate lines are sung by alternate choirs or people.
"Trisagion" - The "Thrice-Holy Hymn" (Holy God, Holy Mighty, Holy Immortal, have mercy on us).
"Proskomede" - the Liturgy of Preparation, where the priest prepares the bread and the wine for the Liturgy. It is done before the Divine Liturgy. See the Wikipedia article
for more information.
"Holy Anaphora" - the part of the Divine Liturgy where the bread and wine are consecrated and become the Body and Blood of Jesus Christ.
"Troparion" - a short, one-stanza hymn. There are Troparia for saints and various feasts. The Paschal Troparion, for example, is "Christ is risen from the dead/Trampling down death by death/And upon those in the tombs bestowing life"
"Kontakion" - a form of hymn. See the Wikipedia article
"Typica" - a short service that is used as a replacement for the Divine Liturgy when it is unable to be celebrated (e.g. there is no priest available).
"The Cherubic Hymn" is a hymn sung at the Divine Liturgy. "Let us who mystically represent the Cherubim, and who sing the Thrice-Holy Hymn to the Life-Creating Trinity, now lay aside all earthly cares, that we may receive the King of all, who comes invisibly up-borne by the angelic hosts. Alleluia".
"Epiclesis/Epiklesis" - calling down the Holy Spirit upon the Holy Gifts (bread and wine) to change them into the Body and Blood of Christ.