Quirky is a lightweight live Linux distribution from the same stable as Puppy Linux. While Puppy is designed for general use, Quirky is far more experimental and is the author's attempt to get back to a smaller distro when everything is growing in size.
Quirky is built using the same "woof" system that is used to build Puppy Linux releases, but the contents are rather different and, in contrast to just about every other distro, are planned to reduce in size with each release.
One of the interesting ideas is to place the entire distro filesystem in an initramfs which is then embedded in the kernel, something now possible with Linux kernels. That would effectively give you an operating system in a file. This hasn't been implemented yet, but it does give an idea of the experimental nature of this distro and the reason for its name.
If you want a small, lightweight distro for general use, you may be better off with Puppy. But if you want something that is also interesting, novel and fun to experiment with, Quirky may be just for you.