Skyshards are collectible items that can be found throughout the world. Except for one in the tutorial quest, collecting Skyshards is entirely optional. However, you will receive one skill point for every three Skyshards you collect.
This is a list of locations by game area, not specific locations, which will be listed on the place pages listed below. Collecting all the Skyshards in one location grants you an Achievement. In-game, clues to each Skyshard's location are listed in the Achievements menu under their respective areas.