Estus Shards in Dark Souls 3 will allow you to upgrade the amount of Estus Flasks you can carry. Estus Flasks will heal your health and focus points which is a new mechanic introduced in Dark Souls 3. You can set the ratio of flasks at Andre the Blacksmith.
There are a total of 15 flasks which you can carry and you need to find around 11 Estus shards in the game to fully upgrade your carrying capacity and also get a trophy/achievement for the same.
All of them can be gotten in your first playthrough itself and they are obviously very helpful and can keep your alive.
Our review of the game can be found here. Check out the video below that shows all the locations.