The Elixir of Life is an incredibly important item and a way for Jinwoo to heal people. However, with it failing to save Haein, the Elixir can only be taken as an item meant to save Jinwoo's mom.

How to use the Elixir of Life. Once you have the Elixir of Life, go to the Upgrades area on the first floor. There, you will find a special place where the units can be evolved.