There will be some resistance in the semiconductor material that causes a voltage to be generated across the device. This voltage is proportional to the current through the diode. Added to this is a voltage, usually less than 1 volt, below which the diode won't conduct in the forward direction. The POWER dissipated in a diode is equal to the voltage across it multiplied by the current through it. So a conducting diode will always get warm. A 5 volt zener will regulate to (obviously) 5 volts, a 25 volt zener to 25 volts. The power rating of the zener is important since considerable power will be dissipated in this type of circuit.