Blast Shards have returned in Second Son, although they are a little different than in previous entries, where they extended your power meter. Instead, they are required to purchase upgrades and new abilities, effectively replacing the XP system from the past games. When you see a Blast Shard, you can use the Touch Pad to absorb it.
Delsin is able to get Blast Shards in a few ways throughout his journey, with the first being the Mobile Command Centers. When you destroy these, they will explode and release four Blast Shards each time. Another way is via the Scanning Stations, which are marked on your map with a hand symbol; blow these up to get a Blast Shard from them.
The last way to get Blast Shards, and the most bountiful, are the Tracker Drones, which are shown as blue dots on the in-game map. These drones are usually flying around a set path, but they can also be found broken. All you have to do is hit them once with any attack, like a normal shot or even a melee, after which you can absorb the Blast Shard.