The vaccine is an anti-"t" reagent, which makes a first and only appearance in Resident Evil 3: Nemesis. After Mikhail sacrificed himself in an explosion with "the pursuer", it returned and fought Jill. She won the battle, but was infected by a tentacle of the creature before her victory. Carlos took Jill to the Clock Tower and left for the Hospital to search for a cure.
This item can be obtained by combining the Vaccine Base and Vaccine Medium together. When Carlos has already created it or he has all items for it's creation and he heads back to the Hospital Lobby, some game triggers are activating. The hospital will blow up, because Nikolai has set up the bombs and shortly after that Nemesis will appear in the clock tower.
To cure Jill, Carlos can just take a dialogue with her, lying on the altar or by using the vaccine near her. After curing Jill, player takes control on her again.