Estus is essentially bottled fire. In the world of Dark Souls, fire is symbolic of life and the power thereof. The current Age, the age of gods (Gwyn, Seath, Nito, The Witch of Izalith, The Pygmy), is also known as The Age of Fire.
When you rest at a bonfire, you capture some of its flame in your Estus Flask. Bonfire themselves are beacons of fire, life, and humanity. This can be evidenced by kindling, strengthening bonfires by sacrificing humanity to them, as well as you regaining health whenever you rest at a bonfire. Thus, whenever you drink from your Estus Flask, you are "consuming" the life held within the flames.