"Biotics" is a term used to both organic lifeforms that developed abilities due to exposure to Element Zero or "eezo", as well as those abilities themselves. Biotics have varying degrees of control over dark energy, channeled through their own bodies, and are therefore have a limited ability to create their own mass effect fields. Several of these abilities seem similar to psionic abilities, such as telekinesis, and it is true that beings with psionic potential can have their abilities increased with exposure to eezo.
Biotic abilities are increased and focused through biotic-amps. These are technological devices implanted into a biotic to help them control their abilities. Biotic abilities can be both destructive or defensive.
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Biotics are derived from Mass Effect.
For canon information, please visit the Mass Effect Wiki.