To understand homeobox genes, lets start by answering this question:
" True or False? Cells in the eye contain different genes than cells in the skin "
The answer is False: With very few exceptions all our somatic (non reproductive cells) are in fact genetically identical. It is refereed to as "genomic equivalence".
So, now the question arises: How do different cell types acquire their unique size,shape and function?
Answer to that is "differential gene expression"
Meaning - different cell types express different sets of genes and that is what accounts for differences between those cell types NOT differences in which genes are present.
(That is a key concept in developmental Biology). Hox genes are actually transcription factors (which activates other genes).
We know that all living things in nature have bilateral symmetry. Homeotic genes are a set of genes within them. So, we have these genes called Hox genes (its reduction of the word Homeobox). These Hox genes regulate the identity of the body segments (create a grand symphony of cellular events). They control (signal) whether or not an area becomes the head or the thorax with mammals ..the vertebrae. The chromosomes are often setup in a linear fashion, so the hox gene reflect that segmentation.