This is a brief guide of where Drupal 7 will look for the template.tpl.php file in a hook_theme item depending on the 'template' and 'path' settings, or lack of.  For a thorough and complete explanation head to the official hook_theme page.

Our setup:

Module: modules/mymodule
Theme: themes/mytheme

We're going to output the value using $html = theme('news_filters').

Configuration 1:

function mymodule_theme() { 
  $themes = array(); 
  $themes['news_filters'] = array(
  ); 
  return $themes; 
}

Drupal looks for file news_filters.tpl.php in themes/mytheme/templates including subdirectories, ignoring the 'template' and 'path' values. If news_filters.tpl.php does not exist and 'template' and 'path' are not set, $html is blank.

Configuration 2:

function mymodule_theme() { 
  $themes = array(); 
  $themes['news_filters'] = array( 
    'template' => 'news_filters'
  ); 
  return $themes; 
}

If news_filters.tpl.php does not exist in themes/mytheme/templates, Drupal will look for news_filters.tpl.php in modules/mymodule.

Configuration 3:

function mymodule_theme() { 
  $themes = array(); 
  $themes['news_filters'] = array(
    'path' => drupal_get_path('theme', 'mytheme') . '/templates',
    'template' => 'news_filters'
  ); 
  return $themes; 
}

If news_filters.tpl.php does not exist in themes/mytheme/templates, setting 'path' will force Drupal to look for the news_filters.tpl.php in themes/mytheme/templates.