The jailbreak is based on yalu by Luca Todesco and provides a full set of kernel patches which allow running unsigned code and injecting arbitrary libraries into any tvOS process.
There is no Cydia; however, the 64-bit version of Mobile Substrate should work. Saurik could release Cydia for tvOS at some point but no word on whether that will happen yet.
The jailbreak will work with any version of tvOS except for 10.1.1. That means that you shouldn't update to 10.1.1 if you haven't already. After jailbreaking you should disable Software Updates to make sure you don't accidentally upgrade to the latest firmware.
Similar to like yalu, the jailbreak most likely will be a binary that needs to be signed with an Apple ID. It is semi-tethered. The IPA includes a modified 64-bit only bootstrap.tar, containing /bin/sh -> /bin/bash, some tools (in /usr/local/bin), dropbear (a free standing ssh daemon, with its keys in /etc/dropbear), and a few select binaries.
Levin says the jailbreak is meant for developers and repeatedly warns that you could easily brick your device.
It's an intentional PoC meant for developers and researchers, not for the general public - and provides 100% the functionality that target audience needs, with minimal disruption of the filesystem. And, because I made the mistake of overwriting a stupid binary (/usr/sbin/nvram), which effectively bricked my older TvOS. I had to fork another $149 to get another ATV box, and - once bitten, twice shy.
We'll let you know as soon as the jailbreak is available for download. Please follow iClarified on Twitter, Facebook, Google+, or RSS for updates.