This makes sense when considering the anatomy of centipedes, which are the animals belonging to the class Chilopoda. Their mouthparts are located on the first body segment, which is called the head. These mouthparts are composed of two pairs of appendages that are modified for biting and chewing.
The name Chilopoda reflects this feature: "Chilo" for "lip" and "poda" for "foot". So, Chilopoda literally translates to "lip-footed".