A pull up resistor provides a constant voltage (and therefore some current) to an input pin on arduino. https://learn.sparkfun.com/tutorials/pull-up-resistors/all A pull down resistor connects an arduino pin to to ground so no current should be flowing through the pin.
When a button is used in a pull up circuit (see ref above) current flows through it only when the button is pressed resulting in a decreased voltage at the arduino pin. When the button is in its native state, the arduino pin sees 5v so more current is flowing through the pin of the arduino. I am simplifying an arduino and thinking of it as a resistor .
Since a button is normally in the open state and spends most of it time this way, if it is used in a pull up circuit, then current is always flowing through the arduino.
A button used in a pull down circuit allows voltage at the arduino pin only when it is pressed, so this seems less wasteful. But apparently, pull up circuits are much more common. why this desire to waste electricity?