The HDR principle is that it takes three or more images at different exposure settings and combines them.
This can be advantageous as we've all had bad photos with overly dark areas in shadow and/or over-exposed sky or other bright areas.
For example using HDR mode you could use a doorway to frame an outdoor scene from inside a building; it would show detail of the door frame and adjacent interior - properly exposed - and still capture a well exposed scene outside.

Selecting that option on your phone, the processing to combine them should be done inside the device and the finished picture is a JPG file just like any others.  
I'm wondering if in your shots that won't open there has been some interruption to the processing - it really should just happen seamlessly in the background but there may be a longer period before you can take another shot. 

It would be good to test it some more but in general it's probably better left off anyway.
The results from doing that processing automatically often look a bit strange and even basic photo software on the computer can lift dark areas and darken bright areas with some success in many photos.