Anapestic means that a line of poetry is composed of anapests, a rhythmic patter that has two light stresses followed by a final heavy stress. Edgar Allan Poe used anapestic lines in Annabel Lee when he wrote For the moon never beams without bring
-ing me dreams
Of the beautiful Annabel Lee.
In the first line the words "For" and "the" are light stresses, and the word "moon" is a heavy stress; that is the first anapest. "Never" has two syllables, and both are light stress, and "beams" is heavy; that is another anapestic unit. "Without" also has two syllables and they are light, but "bring" is heavy stress. (Note that the line is split to show that a new stress pattern begins with the light stress of "ing" and "me" and the heavy stress of "dreams."
This is a rhythmic pattern, just like a song, so sometimes it helps, if you have to write an anapestic line, to see if you can hum and keep the beat in the lines you are considering without forcing the sense or the diction or the syntax of the line.