Your app store may be showing updates because you are running an old OS.
For example, you may be running apps that realise they need updating, and so the app store badge reflects this.
But when you go to update your apps, the device realises that you're running an old operating system, and so it can't provide the updates for you to download.
The solution: Simply update your operating system! (you may need to clear some space in order to do this).
If you've got a phone that doesn't support the latest software, sorry but you may need to consider an upgrade.