Hi,
Welcome to Microsoft Community.
The issue you have reported is you are unable to update apps. We need some more information to assist you in a better way.
1. Which app are you trying to update?
2. Have you installed any third party security software on the computer?
3. Is the issue confined to particular app?
4. Do you have any issues installing Windows update?
5. Have you set any proxy to connect to Internet?
6. Are you connected to any network?
7. Did you make and changes prior to the issue?
Let’s try few methods which might help us in resolving the issue with updating the apps.
Method 1: Please run troubleshooter to resolve issues with updating apps.
Download and run the Modern UI App troubleshooter and check.
http://download.microsoft.com/download/F/2/4/F24D0C03-4181-4E5B-A23B-5C3A6B5974E3/apps.diagcab
Method 2: You may try to reset the Windows Store cache.
a. Press Windows key + R to open run window.
b. Type wsreset.exe.
c. Press OK.
Method 3: Check the proxy settings in Internet Explorer.
Follow the steps to disable proxy, if it is enabled:
a. Click the Gearbox at the top right corner in internet explorer.
b. Click the Tools button, and then click Internet Options.
c. Click the Connections tab, and then click LAN settings.
d. Uncheck the box next to “proxy server for your LAN”.
e. Click OK to save and close the window.
Method 4: Temporarily disable third party anti-virus and check if this helps.
Important Note: Antivirus software can help protect your computer against viruses and other security threats. In most cases, you shouldn't disable your antivirus software. If you have to temporarily disable it to install other software, you should re-enable it as soon as you're done. If you're connected to the Internet or a network while your antivirus software is disabled, your computer is vulnerable to attacks.
You may refer the link for additional information:
http://windows.microsoft.com/en-us/windows-8/what-troubleshoot-problems-app
http://windows.microsoft.com/en-US/windows-8/why-find-install-app-windows-store
http://onlinehelp.microsoft.com/en-us/ais/hh309450.aspx
Hope this helps. For any Windows related queries or issues, please get back to us. We are here to assist you.