The short answer is it's a bit like Fedora, as for the long answer, read on...

A bit of a history lesson, if I may. Sailfish is the continuation of the MeeGo project, a partnership formed between Nokia and Intel, after they merged their maemo and Moblin projects. maemo was based on Debian, while Moblin was built on Fedora. As they went down the route of using RPM software repositories, I think I'm correct in saying MeeGo was a little closer to the Fedora side of things.

When the MeeGo project was abandoned, the Mer project was reanimated, forking that work. Mer is more of a core or middleware, upon which vendors add on a UX (in Jolla's case Silica) and use a kernel. Packages are built using the OpenSUSE build service.

So to answer your question, Sailfish is built on Mer. As it uses the Wayland display server protocol (as opposed to X), with Lipstick as it's graphical shell framework, in reality there isn't a distribution that is really close to it, although Fedora keep projecting future releases which will use Wayland. There are also similar philosophies, eg early adoption of new technology (wayland, systemd, etc).