https://site.online/admin/structure/taxonomy/{name}/fields

Description replace

replace fields with changable items

https://site.online/admin/config/regional/entity_translation

https://site.online/admin/config/regional/i18n/select

Additional possible SETTING:

for the title: {region.tpl.php}

<h1 class="title" id="page-title"><?php

    if(arg(1) == "term"){ //check if it is a taxonomy page
      $tid = arg(2);
      $term = taxonomy_term_load($tid); //load the term
      $term = i18n_taxonomy_localize_terms($term); //ask for the translation
      $title = $term->name; //assign the translated name to the title
    }
   print  $title; ?></h1>

for the description: {node.tpl.php}

<div class="content">
    <?php
       $term = i18n_taxonomy_localize_terms($term);
       $content['description']['#markup']= $term->description ;
       print render($content); ?>