It means eReaders that use Linux as their operating system, e.g. Kindle, Kobo, Remarkable. They don't give you root access out of the box, they don't run standard Linux applications out of the box and I'm pretty sure they don't use standard mainline kernel because usually these kinds of devices require some sort of binary blob driver for something.
Getting standard Linux applications on one depends on the device. Some like Kindle are more locked down. Others are a bit more open. None are really "open" like a standard PC linux distro.
The Remarkable 1 has been hacked to run a linux desktop recently.
It's actually easier to get an Android eInk device running desktop Linux applications through an X11 server and a proot than it is to get one up and running on most Linux eReaders.