As Daniela mentioned, we only show the category description in the dropdown for new users (trust level 0) and it’s hidden for everyone else. The thought is that regular visitors will benefit from seeing more categories at once and the descriptions are less useful.
You can override this behavior by adding this to the head section of your site’s theme (admin > customize > themes > edit html/css):
<script type="text/discourse-plugin" version="0.8">
api.modifyClass("component:category-drop", {
displayCategoryDescription: true,
});
</script>