How to Install Ubuntu on Android! states "your Android OS must support loop devices". What is a loop device?
The Wikipedia page on loop devices explains this pretty well. It's basically a "pseudo-device" (i.e. a device which doesn't exist physically) that allows a file to be treated as a block device (for example, a hard drive).
You need support for it because the Ubuntu system is stored as a .img file, which is essentially created to be a file representation of a filesystem or disk partition. By mounting it on a loop device you can access the file as though it really was a whole filesystem, thus creating a sort of "virtual" partition (or disk) for Ubuntu to live on.
In Unix-like operating systems, a loop device, vnd (vnode disk), or lofi (loopback file interface) is a pseudo-device that makes a file accessible as a block device.
Basically, it allows you to make your phone think that an image file is a separate storage area/device.