The physiology of the Immortals is somewhat odd, as on their home planet they are not truly immortal. They are only immortal whilst they are on the planet Earth, during which they can only be killed by severing the head from their body and "The Quickening" takes place. If "The Quickening" does not take place, then the immortal will come back.
Also they are only immortal when there is more than one Immortal occupying the planet - when one Immortal kills another on Earth all the strength, memories and attributes are passed on to the victor; this phenomenon is called "the Quickening". When there is only one Immortal left on Earth they become mortal once again until another Immortal from Zeist arrives on the planet.
The Immortals seem to have some knowledge of Earth culture, and for unknown reasons are forbidden from fighting on holy ground.