Here's why:
* Adjectives describe nouns. For example: "The *light* box" (light describes the box).
* Adverbs describe verbs, adjectives, or other adverbs. For example: "He walked *lightly* across the room" (lightly describes how he walked).
In the sentence "He walked lightly across the room," "lightly" describes the manner in which he walked, making it an adverb.