What is the meaning of chicken with their heads cut off?

A chicken with its head cut off tends to still run around aimlessly for several minutes after death. This is because the nerves in the body are still active for a short time. The saying "like a chicken with its head cut off" is a shortened version of "running around like a chicken with its head cut off" or, in the Australian vernacular, "running around like a chook with its head cut off".

This means that someone is very active, flitting at high speed from one activity to another, sometimes in nervous agitation. Their actions seem random as they try to cover everything they possibly can in as short a time as possible.