Undead Bone Shard will allow you to increase the potency of your Estus flask so that it can heal more health and focus points. As your health and focus points bar increases you would need each flask to heal more so you need to find this and burn it at the bonfire. To increase Estus Flask capacity you would need to find all Estus Shards.
Finding all Undead Bone Shards will unlock a trophy/achievement. There are a total of 10 shards to find which are found in easy locations but considering the game is huge it will take a while to find them all on your own. However, we have a video that shows the location below.
Our review of the game can be found here. Check out the video below.