A stalk is a wooden handle (that botanists call a raceme) that carries female flowers, and therefore the palm fruits at different phases of growth and ripening. As the stalk is full of fruits, it is called a cluster, but once the fruits are harvested, it dries up, develops a hard texture, and takes on the shape of a crescent. That is where the Quranic comparison of the crescent to an old stalk comes from.
(And the moon – We have determined for it phases, until it returns [appearing] like the old date stalk.) [Yaseen: 39]