Note: the tutorial applies to PrestaShop v1.4.7.3 and below. The bug has been fixed in PrestaShop v1.4.8.x
It only occurs if you have module override in /themes/themeXXX/modules/module_name folder
If you have applied translations under Tools -> Translations -> Module Translations section but they are not displaying on Front End but do display in PrestaShop admin you should do the following:
1. Translate all the modules under Tools -> Translations -> Module Translations section in your PrestaShop admin panel.
2. Navigate to /themes/themeXXX/modules/module_name folder.
3. Here you should see language files. The file name is XX.php where XX is the language code (e.g. en.php). The filesize should be 0 (zero).
4. Delete all the language files under /themes/themeXXX/modules/module_name folder.
5. Repeat steps 2-4 for all the modules you have in /themes/themeXXX/modules folder.