Blast Shards return in Second Son, although they function a little differently than in previous games. Instead of extending the power meter, Blast Shards in this game are used to purchase abilities and upgrades, effectively replacing the XP system in the past. You must absorb the Blast Shards using the Dual Shock 4's touchpad in order to collect them.
Delsin will be able to find Blast Shards in a few different ways. There will be drones of sorts flying around that Delsin can shoot down (one normal shot will do); they fly a predetermined path. Another method is from Scanning Stations, which you encounter early in the game. You can blow these up, then you can absorb the shard. The last method is by destroying the Mobile Commands in each district, each of which house four shards.