live-initramfs is a collection of scripts providing hooks for the initramfs-tools, used to generate an initramfs capable of booting live systems, such as those created by live-helper. This includes the Debian Live isos, netboot tarballs, and usb stick images.

At boot time it will look for read-only media containing a "/live" directory where a root filesystem (often a compressed filesystem image like squashfs) is stored. If found, it will create a writable environment, using aufs or unionfs, for Debian like systems to boot from.

live-initramfs is a fork of casper.

More information on initial ramfs in Debian can be found in the Debian Linux Kernel Handbook's chapter on initramfs.