How do I see version numbers of my apps on iOS?
On your iPhone:  


Open the Settings app  
Go to General->Usage  
Under the Storage section, wait till it shows the list of apps  
Click on the app you're interested in to see the App Version, the App Size and the amount of data it has stored on the device.


This works only for third party apps. The Apple provided stock apps will not show this information.



In iOS 11 the method described also works for Apple provided stock apps.