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Depletion width is the width of the depletion zone in a p-n junction. The depletion zone within a semiconductor device is a region of nonconductor whose width can be controlled by e-fields, i.e. by applied voltage.
Here is a more intuitive picture. When an n-type semiconductor is brought into contact with a p-type semiconductor, the n-type carriers will move into the p-type region. Vice-versa, the p-type cariers will move into the n-type region. This causes a charge imbalance and therefore a voltage across the junciton. The depletion width is the width of the region where the carriers from one type of semiconductor bleed into the other. It is the distance over which the contact potential drops.
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