It sends an electrical impulse through the body.
Since muscle is predominantly water, and electricity travels through water faster, the quicker the signal returns back, in theory the leaner you are.
However, hydration levels play a big role in their consistency as well as accuracy.
I think it's best to have a person do skinfold pinches when possible, but if you're stuck using the scale just try to be consistent with water intake, the time of day you take readings as well.
I had a skinfold done (7 site) and then immediately tried the scale. The scale gave me a reading of double that of the skinfold, needless to say I'm not a big fan of electrical impedence devices.