The "magical thing" is input impedance. This means, the amount of resistance the input has. For CMOS and other digital inputs, the input impedance is very high - megaohms or more - meaning that any tiny thing (even stray electrons) can influence it. Which is why it is so sensitive to noise. But tie a 10k pull-down to it, and the noise and stray electrons are much smaller than the pull-down, so never cause the input to leave "low" status.
Another analogy might be that of a small gasoline (petrol) engine. A weak spring (pull-down) is used to normally keep the throttle at idle speed. Increase the throttle (against the weak spring), and the engine accelerates. So what happens if this spring is removed? It only takes a microgram to turn the throttle valve - the engine may accelerate to any speed or even oscillate because the valve is SO sensitive.