Causes of monozygotic twins
A few possible explanations are named in the Wikipedia article you link:


  Regarding spontaneous or natural monozygotic twinning, a recent theory
  posits that monozygotic twins are formed after a blastocyst
  essentially collapses, splitting the progenitor cells (those that
  contain the body's fundamental genetic material) in half, leaving the
  same genetic material divided in two on opposite sides of the embryo.
  Eventually, two separate fetuses develop. Spontaneous division of
  the zygote into two embryos is not considered to be a hereditary
  trait, but rather a spontaneous or random event.
  
  Monozygotic twins may also be created artificially by embryo
  splitting. It can be used as an expansion of IVF to increase the
  number of available embryos for embryo transfer.


Interesting references for this are:


"The epidemiology of multiple births"
Twinning.
On the possible cause of monozygotic twinning: lessons from the
9-banded armadillo and from assisted reproduction.
Monozygotic twinning associated with assisted reproductive
technologies: a review.
Developmental biology: Two by two (on overview article conatining a
lot of other references)