what is use of $title_prefix and $title_suffix variable inside drupal theme system
I'm not sure how it could be any clearer than on the docs page, but here goes;


$title_prefix is for content that should be displayed directly before the title in a template file (node.tpl.php, block.tpl.php, etc).
$title_suffix is for content that should be displayed directly after the title in a template file.


There really is nothing more to it than that. If you choose not to include these variables in your template file then they simply won't be rendered.

Since any module/theme in the system has the chance to populate/change the values that are in either of these variables it's impossible to say exactly what will not be rendered in your particular case if you choose not to display them. 

As an example, (and if I remember rightly), contextual links for blocks/nodes are contained in the $title_prefix variable. So if you don't print $title_prefix in your template, you won't get contextual links for that item.