I have been researching the inner workings of my bioelectrical impedance scale. I understand, basically, that it measures bodyfat by inference, based on the relative water composition of fat, bone, muscle, etc.
"A significant fraction of the human body is water. This body water is distributed in different compartments in the body. Lean muscle tissue contains about 75% water. Blood contains 83% water, body fat contains 25% water and bone has 22% water."
The bodyfat measuring scale simply measures impedance and resistance, or the rate at which electricity can flow through a substance: electricity does not flow through fat, and adipose tissue is about 83% fat. The current largely flows through the path of least resistance, or tissues such as muscle and and blood which are mostly water. The amount of fat in the body mostly determines the resistance and the amount of lean tissue mostly determines the impedance of the current: this allows the scale to more or less take a reading of the body's fatness.
After reviewing the science behind this, I can say this is a massive oversimplification, for more information than you really want to know, see HERE.