It is first used to collect acid from a large pot found in the Kitchen area of the Prison in the Northern Block. Using any other type of glass vessel to collect the acid will prove useless, as only the Glass Jar can be used to properly collect it due to the jar's large opening, as opposed to any other glass bottles found in the game. Once the jar is filled with acid, the acid must be used to weaken a padlock, thus being able to pass a gate leading to the Cistern Entrance.
Once in the Cistern Entrance, it must be used to collect oil, which is used to loosen a lever that's required to lower a much needed ladder. It will remain empty and unused from this point on in the game, unless the player chooses to make the life saving tonic for Agrippa.
If the player chooses to make Agrippa's tonic, the jar must first be combined with a piece of string (found in the highest level of the Transept), then used to collect a tortured victim's blood in one of the Transept's torture chambers. In a laboratory found in the Nave, the blood in the jar must be boiled and purified to extract Vitae, then combined with a poison gland and Tampter from a saliva-covered bone. If only one or no ingredients are added to the purified blood, an unusable "incomplete tonic" is left in the inventory. If all ingredients are combined, the player is given the usable tonic.
The use of the completed tonic is entirely optional. It can be fed to Agrippa, or can continue to sit in the inventory given that the player suddenly decides to not use it. If the tonic is fed to Agrippa, he can have his head removed without dying, which in turn can be placed in Alexander's portal at the end of the game. The tonic/jar disappears from the inventory if Agrippa is given it.