Amazon has listed "technical reasons" as to why eink is easier on the eyes than LCD. Here are the reasons.
Ambient brightness: Every time your eye switches from a bright screen (like LCD) to the dimmer ambient room, your eyes adjust which may result in fatigue. With E Ink, the page is the same brightness as everything else in the room so there's no adjustment needed.
No parallax: Parallax is the apparent displacement of an observed object due to a change in the position of the observer. Text on an E Ink screen does not appear to shift at different viewing angles.
Less glare: All E Ink surfaces are treated to be matte like a printed page. Most LCDs are not, which creates glare and decreases legibility.
Uniform contrast ratio: The contrast ratio of an LCD varies detectably with viewing angle. E Ink's contrast is uniform, so you can read comfortably at any angle.
No aperture ratio loss: LCDs have tiny black gaps between each pixel, but E Ink screens have 100% aperture ratio. The blacks and whites on an E Ink screen are uniform, improving image quality.
I know that eink vs lcd threads have been done before, but I want to address what is specifically listed on the Kindle page at amazon.