Final answer:
The parotid glands are the ones that swell in mumps, leading to the typical appearance associated with this viral infection.
Step-by-step explanation:
In mumps, the glands that swell to produce the disease's characteristic appearance are the parotid glands. Mumps is caused by the paramyxovirus, which targets the parotid glands situated near the ears and jaw, resulting in inflammation and enlargement that is visible externally. These glands are part of the salivary glands and are responsible for producing saliva containing salivary amylase, which aids in digestion. Mumps patients often experience symptoms like fever and throat pain, the latter of which can be exacerbated by acidic substances like orange juice, due to the proximity of the swollen parotid glands to the throat area.