The lyric from “O Christmas Tree” is “How lovely are thy branches,” so the stored answer is branches.
The English song is a version of the German “O Tannenbaum,” whose title literally means “O fir tree.” The modern German lyrics were written by Ernst Anschütz and published in 1824, building on an older folk tradition. The song was not originally a Christmas song in the modern sense; it praised the evergreen fir as a symbol of constancy and faithfulness.
Earlier versions contrasted the tree’s steadfast greenery with an unfaithful lover. As decorated Christmas trees became increasingly popular during the 19th century, the song became associated with Christmas and was adapted into English. That history explains why versions may mention branches, leaves, or greenery in different translations.
In the standard English lyric, however, “branches” is the accepted continuation. Garlands, needles, and candles appear in other Christmas-tree imagery or alternate verses, but none is the canonical answer to this question.