When there is a new update available for your Windows Phone 8, you get the notification for this in the settings. You can download and install the update and this process has many steps. First is to download the update, secondly to prepare for installation and then we have the actual installation process and finally after rebooting the phone, the update will migrate your apps to the new environment. But sometimes the final step of migrating apps might be just skipped for some reasons and hence you wont be able to open any installed apps on your phone. This means all apps not native to the OS (i.e.. people hub, photos, etc.) will not open, only the native settings and apps open.
So how do your solve this issue? Since the update is installed successfully, you cannot install it again. Further, you cannot solve this problem with soft reset, you will have to do a hard reset which will end up having to install all your apps again. But there is a simple work around and it involves forcing an update to Windows Phone.
So, in order to force the update, you need to install a new keyboard to your phone. This can be done by going to Settings-> Keyboards. Now click on the option Add a keyboard and select a keyboard which shows you the download size. This means that the keyboard will be downloaded through Windows Phone updates.
Now this will download the keyboard on your phone and once the download is complete, your phone will show a new update available for your phone. Now install this update (the keyboard). Your phone will follow all the process of normal update including migrating the apps and preparing it. Finally you will see that the keyboard update will automatically migrate apps and this solves the issue.
In case you are facing this issue after updating your phone, you can try out this simple fix instead of resetting your phone and installing all apps again.