Final answer:
Between the palatoglossal arch and the palatopharyngeal arch lies the palatine tonsil, a lymphoid tissue that forms part of the immune system.
Step-by-step explanation:
The structure housed between the palatoglossal and palatopharyngeal arches is the palatine tonsil.
The palatoglossal arch is a muscular fold that extends from the lateral side of the soft palate to the base of the tongue, while the palatopharyngeal arch extends from the lateral side of the soft palate to the side of the pharynx, forming the superior and lateral margins of the fauces. Between these two arches lie the palatine tonsils, which are clusters of lymphoid tissue that play a key role in the immune response by trapping and destroying pathogens entering through the oral or nasal cavities.