Wow, people commenting seem to have so little information about what this actually is. (Canonical is partly to blame for, as usual, doing a poor job at messaging.)
This is not replacing the Debian build system or Debian packages. Ubuntu will continue to be based on Debian.
This is an additional packaging system that makes it exceptionally easy to more reliably distribute Linux applications and services. Underneath it uses LXC (also originally developed at Canonical), the same jail-like technology that powers Docker and LXD. It basically lets the application get its own "view" of the operating system's filesystem (using AuFS) so that you can distribute required dependencies with the application. Of course it can't override the Linux kernel or other important system services, but it actually solves a major hurdle in distributing software across various OS library baselines. Until now, we've been using PPAs or other external Debian repositories to distribute software -- you can still use them if you prefer, but these are tied to the baseline and need constant tweaking to the packagers. A Snappy package made now should be able to run years from now without a problem. The Snapcraft packaging tool is very easy to use and does so much of the hard work for you: you can even just give it a git repository URL, and it will pull and build and package. I see it being very useful for something like Steam.
Also, like Docker, Snappy uses SHA-signed diffs, so package updates will be very fast. It also makes it trivial to switch between versions.
The announcement is that Ubuntu 16.04 will come with Snappy built in, so you can immediately install Snappy packages if you want. You don't have to.
There is also a new flavor of Ubuntu called "Snappy Ubuntu Core" in which the base OS itself is a Snappy image, so that it gets updates the same way as the other packages, and in the same way you can switch between versions. It is useful for various special use cases. For example, a phone OS will have an easier and safer job upgrading while letting the user trivially revert back if things break. It is not the official Ubuntu recommended for all users, but rather a building block for developers to create specialized Ubuntu-and-Snappy-based distributions.