The original BioShock and its sequel, BioShock 2, featured what the games referred to as Plasmids. These Plasmids were drinks that you could consume to gain superhuman powers, such as the ability to shoot fire from your hands, freeze water, and summon a swarm of angry wasps to destroy your foes. These Plasmids were created through the discovery of ADAM, which was harvested from underwater sea slugs. Humans became addicted to these powers and that subsequently lead to the downfall of Rapture, or so the story goes.
BioShock Infinite does not have Plasmids, but it does have its very own set of magical powers, referred to as Vigors. Like Plasmids, you have to consume them from a bottle and they'll bestow upon you superhuman abilities that allow you to strike down your foes with lightning from your hands, or even summon a murder of crows to peck their eyes out.
You'll find these Vigors all throughout the game at various checkpoints. Beyond using these Vigors, you'll also have the opportunity to upgrade them at vendor stations located in the game.
The following video, produced by PowerPyx, serves as a guide on how to find them all.
#1 – Possession Vigor – 0:05
#2 – Devil's Kiss Vigor – 0:29
#3 – Murder of Crows Vigor – 0:48
#4 – Bucking Bronco Vigor – 1:05
#5 – Shock Jockey Vigor – 1:26
#6 – Charge Vigor – 1:49
#7 – Undertow Vigor – 2:15
#8 – Return to Sender Vigor – 2:47
These Vigors are also tied to two achievements and trophies called Well Rounded and Combination Shock.