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A diode is a semiconductor device that allow current to flow only in one direction. However, its different in case of a zener diode.
Forward and reverse diode :-
Never heard of it but if you mean forward and reverse biased diode, it is direction in which the higher voltage is connected to cathode or anode. When the positive is connected to the anode and negative is connected to the cathode(difference must be greater than 0.6v for silicon and 0.3v for germanium diode), current flows from anode to cathode. This is known as forward bias.
When the positive(high potential) is connected to the cathode and the negative (low potential) is connected to the anode, this condition is known as reverse bias. Usually, there is no flow of current. However, if the positive voltage is increased across the cathode to anode, the diode encounters a breakdown where it gets destroyed. Its different only in case of zener diode.
In Zener diode, current flows in reverse bias condition only when the cathode voltage is greater that the specified voltage(2.2 to 200 volts in common depending on the diode) known as the Zener voltage. The zener diode in reverse biased condition does not allow current to pass unless the potential reaches the Zener voltage. When the Zener voltage is reached, current flows in reverse bias across the diode.
For more info on depletion region in diode, see this :-
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/pnjun.html
http://www.daenotes.com/electronics/devices-circuits/formation-depletion-layer-diode
Hope that helps.
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