The twenty-four elders fall down: as in 1.17, to fall down means to kneel down or to lie prostrate on the ground.
Before him who is seated on the throne and worship him who lives for ever and ever: this repeats from the previous verse the two phrases that describe God. This repetition is very much a part of the style of the author, and a translation should not try to abbreviate the text by omitting what seems to be unnecessary repetition.
Worship: to worship is to acknowledge the unique status and worth of the one being worshiped, and the relationship of that one to the worshiper. Louw and Nida, Greek-English Lexicon (volume 1, page 540), define as follows: “to express by attitude and possibly by position one’s allegiance to and regard for deity.” The Greek verb used here may mean “to kneel before” (see its use in this sense in 3.9, “bow down”). However, the elders are already lying prostrate before the throne, so “kneel before” is an unlikely meaning here. A possible alternative rendering for worship is “and acknowledge his greatness.”
They cast their crowns before the throne, singing: this action acknowledges that God is the supreme King, who rules over them. Crowns represent their power, authority to rule as kings, and so here they surrender their power to God. The verb has the forceful meaning of “throw,” and it seems better to represent this meaning than to say something like “lay” (Revised English Bible) or “lay down” (Translator’s New Testament). The Greek verb translated singing by Revised Standard Version is “saying” (Good News Translation). In many languages this clause will be rendered as “they throw their chiefs’ hats down in front of the high chief’s chair.”
Quoted with permission from Bratcher, Robert G. and Hatton, Howard A. A Handbook on The Revelation to John. (UBS Handbook Series). New York: UBS, 1993. For this and other handbooks for translators see here .