Adrenaline is a value like health and power. Like power, it is used to activate certain abilities. Some adrenaline-powered abilities (like sprint) slowly drain adrenaline while they are in use. Others use it in chunks, similar to the way power is used. Each of the tier 4 classes also has one signature ability that requires a full bar of adrenaline to activate.
Adrenaline is accumlated as you kill enemies in battle. Loss of adrenaline is one of Tabula Rasa's death penalties. Upon resuscitation after death, the entire adrenaline bar is drained.