What exactly is this and what does Linux have in relation to tails?

Tails is a privacy-focused GNU/Linux operating system, more specifically a Debian-based distribution. It "ships with several Internet applications, including web browser, IRC client, mail client and instant messenger, all pre-configured with security in mind and with all traffic anonymised. To achieve this, Incognito uses the Tor network to make Internet traffic very hard to trace"(source). You can either install it on your hard disk, boot it in live mode from usb/dvd(not permanent) or even create a VM (virtual machine) and try it from within your current OS. Installation how-to and downloadable images are available on the project's website