How to use jquery to show divs based on select box?
you ommited the drupal.behavior, that s probably why it doesnt do anything.
And i would suggest working with classes instead changing style. In your css you create a style with visibility:hidden, apply it to each element and then remove it on click. (and add it again once you clicked on something else ...)

document.getElementById doesnt make much sense there ... you can write it better like this : 

(function($){
Drupal.behaviors.taxdescGetDesc = {
  attach: function (context) {
    $("").click(function(event)){
    option = $(event.currentTarget).val();
    $('#'+option).removeClass("hidden");
  }
}