Why is calamine solution applied on the skin where an ant bites?

Neutralization. Calamine solution contains zinc carbonate (basic ph) and ant's sting contains formic acid. The reaction between the acid and the base neutralizes the effect of the sting. Taking an oral antihistamine such as Benadryl (diphenhydramine) or Claritin and applying a topical steroid cream also help.
Stops the itch. Calamine lotion stops the itching caused by ant bites. You will need to apply it several times a day.
To reduce itching. Calamine is a combination of zinc oxide and ferric oxide or zinc oxide and zinc carbonate which helps reduce itching. Calamine is a mild antiseptic and astrigent.