The developmental gene family that controls body segmentation in animals is the Hox gene family, commonly called Hox genes. These genes help give different sections of an embryo their identities along the head-to-tail axis.
Hox genes encode transcription factors, proteins that switch other genes on or off during development. In many animals, their order along a chromosome broadly corresponds to the order in which they act from the front of the body toward the rear. This unusual arrangement is known as collinearity and helps coordinate the formation of repeated structures, such as vertebrae or appendages.
Hox genes are part of the larger homeobox gene group, which is why Homeobox can seem like a tempting answer. The terms are not interchangeable: homeobox describes a DNA sequence found in many developmental genes, while Hox genes are a particular family of homeobox-containing genes. Pax genes and MADS-box genes are also important developmental regulators, but they are not the canonical answer to this segmentation question.