Estus Flask

Ingame Description
The Undead treasure these dull green flasks. Fill with Estus at bonfire. Fills HP.

The Estus Flasks are linked to the fire keepers. The Dark Tales also make reference:

An esmerald flask, from the keeper's soul She lives to protect the flame, And dies to protect it further.

Use
An item that restores health when consumed. Unlike the Grasses in Demon's Souls, the Estus Flasks can be replenished after being consumed, when resting at Bonfires

Number of Flasks
The number of flasks restored when resting at a bonfire depends on whether or not the bonfire has been kindled at before. Kindling a bonfire results in five more flasks being given whenever rested there, with five more for each additional kindling. If you rest at an un-kindled bonfire and have more flasks than the minimum number of flasks for that bonfire, you will keep the number of flasks you have; the game will not take away your extra flasks. Bonfire Kindling Level Flasks Restored

You must obtain the Rite of Kindling from the Pinwheel Boss in the Catacombs to be able to Kindle Bonfires beyond 1 time.

Upgrading
Estus flasks can be upgraded to refill more HP. You must first attain a Fire Keeper Soul and then give the item to Anastacia of Astora below the Firelink Shrine. The Witch that you talk to in order to join the Chaos Servant covenant can also upgrade your flasks.

The maximum Estus Flask level is +7 (needs confirmation).

Health Replenishment
Every upgrade of Estus Flask refills a static amount of HP. Estus Flask Level HP Restored