A Flatpak is a type of cross-distribution packaging format that is managed (including installation, configuration, upgrading, etc.) with its own package manager that is invoked by the flatpak command. This package manager is dependent on systemd, so is only suitable for systems like Fedora that have systemd installed. Other distributions that come with systemd pre-installed and Flatpak in official or unofficial (yet still maintained) repositories include: Arch Linux, Debian (Jessie backports, testing, unstable), Mageia, openSUSE Tumbleweed (openSUSE Leap 42.1 and 42.2 have an unofficial repository with an outdated version of Flatpak) and Ubuntu 16.04 and later.
While Flatpak is not officially affiliated with the Fedora Project, or GNOME Foundation, it is perhaps best supported by Fedora and the GNOME desktop environment. This is because Fedora releases 23 and later have all had Flatpak in their official repositories. The GNOME Software application also has support for installing Flatpaks.