How to update Drupal modules and Drupal core
Some Drupal modules you can update under path: /admin/modules/update
But some modules and also core is not posibble update from administration section.
Then you need to do that manualy.
If you have installed Drupal Administration menu module, you can see available updates under this section.
Try to update all modules from here first and those modules which you are not able update you need to manual download from particular links and then you copy them into location: /sites/all/modules/
This is path for all custom Drupal modules.
Don't forget add your site into maintenance mode under this path: /admin/config/development/maintenance
When you are done with copying new modules, then you need to run update.php which. It looks like this: www.yourdomain.com/update.php
Continue until you'll see page that confirm you are done with update and you can check if is your Drupal site up to date in section: /admin/reports/status
Don't forget put your site to online in maintenance page and also backup before you're doing update.