Final answer:
Eosinophils are the cells that mediate hypersensitivity reactions and can damage parasites. They release toxic substances and antihistamines that help fight parasites and allergic reactions respectively.
Step-by-step explanation:
The cells that are important mediators of hypersensitivity reactions and contain substances that can damage and kill some parasites are eosinophils. Eosinophils are non-phagocytic leukocytes related to neutrophils and are highly effective against large parasites, such as worms, by secreting toxic substances. These cells also play a role in allergic reactions, as they contain granules with molecules that can act as antihistamines, counteracting the activities of histamines from basophils and mast cells.