Lil'Debi is an Android application while allows you to run Debian Operating system in parallel using chroot. It uses cdebootstrap to build up the disk image, and also provides start and stop methods for handling mounting, fsck, starting/stopping, etc.
It is not simply a chroot manager, but it also transparently integrates Debian and Android, example: If the ssh-server in installed in Debian you can login directly using the phones IP address. The Android devices are also mounted inside the Debian. You can even configure auto start/stop of the Debian OS with Android.
Usecase:
install a complete python dev environment on your tablet
run a wordpress server with built-in UPS on your old phone
You can apt-get install anything that Debian has to offer, including all sorts of services like HTTP servers, SSH, etc. Here's the start of a catalog of what's working now
sshd
dropbear
lighttpd
mysqld
nginx
samba
quasselcore
Source code: https://github.com/guardianproject/lildebi