The poetry term acephalous comes from the Greek a-, “without,” and kephale, “head”—hence “without head.” The word also comes up in biology to denote animals without heads—for example, “acephalous worms.”
In poetry, a line of verse is acephalous when it’s missing an initial syllable suggested by the poem’s meter. This is also known as a headless line.
For example, these lines are from A.E. Housman’s “To an Athlete Dying Young,” which has an 8-syllable, 4-accent metrical scheme:
Man and boy stood cheering by,
Townsman of a stiller town.
Cannot see the record cut,
Each of these lines begins with a strongly accented syllable, and each is immediately preceded by a line ending in a strongly accented syllable. The silent unaccented syllable fits between the two accented syllables.