Why does the width of the depletion region of a p-n junction diode increase when it's reverse biased by connecting it to an external voltage source?
In a somewhat simplistic explanation, since the N side is connected to the positive side of the external voltage source, electrons are attracted to that positive terminal. The same goes for the holes in the P side being attracted to the negative terminal. With an excess of electrons and holes at the end of the PN junction there is a buildup of positive and negative ions at the depletion region making it wider. @Debasis buxy is also correct about the E field strengthening.
This is a great site to explain both forward and reversed bias with some excellent diagrams: http://conceptselectronics.com/diodes/diode-biasing/
Hope this helps!
Check these out also or search for "energy bands in PN junction" or "potential energy barrier in PN junction" http://hyperphysics.phy-astr.gsu.edu/hbase/solids/pnjun2.html http://ecee.colorado.edu/~bart/book/book/chapter4/ch4_2.htm