How to show taxonomy terms' description field on a node/add form instead of term title only in drupal 7?
The following solution slightly alters your requirement. Instead of having the term description field showing up as part of the term select widget, create a view block set to be visible on node/add pages which provides a table listing of each term and its description field.

To do this, create a new view of type "Taxonomy." It will have two fields: taxonomy term, and taxonomy term definition.

You could put help text associated with term_reference field which alerts the user to the block which holds the terms and description.

It would be very difficult to alter any select widget to include the description field in a way that wouldn't make a mess of the page.