The Prime Barrier is a part of the physiological makeup of Homo superior that prevents them from deliberately killing a living thing.
Original Series Edit
1990's Series Edit
In the first series, while talking to Lisa Davies aboard the The Ship, Adam Newman confirms the existence of the Prime Barrier in the series (though they don't give it a name) while relating how he got a shark bite because he was unable to defend himself from a shark even though he had a knife at the time.
Despite this, the Tomorrow People in this series do appear to overcome the Prime Barrier in places. This is usually indirectly, such as Adam intentionally saving an antidote instead of Dr Culex when she fell off a railing, resulting in her death. However, in the episode "The Living Stones" the team does intentionally destroy a group of hostile alien invaders.
U.S. TV Series Edit
In "Limbo", a Tomorrow Person named Michael turns out to be a serial rapist. He beats Stephen unconscious, then throws him into a sewer. This shows that the Prime Barrier only extends to the deliberate taking of a life, and does not prevent causing physical or mental harm, nor actions that indirectly result in death.