It actually takes 3 quick pictures: one is properly exposed (well according to the software), one is over exposed, and one is underexposed. The 3 images are blended together to make one with more dynamic range than just a single photo from this camera can provide.
Nexus5
That is what a normal HDR mode is supposed to do. But then Google's HDR+ in the Nexus 5 isn't a normal HDR mode.
It is simulated HDR. True HDR shots are taken by bracketing the exposure (shutter speed) of an SLR camera (part time photographer here). A cheap little image sensor in a phone can't do this, so it simulates over exposure and under exposure by taking a longer or faster shot from the sensor. Then the camera software automatically combines the images. In a true HDR photo, you need some decent software to merge the bracketed images together, and this usually takes time to tweak everything by hand to make it not looks like ass (see /r/****tyhdr for plenty of examples on how NOT to do this).
Anything claiming to be HDR that is not taken from proper bracketing on an SLR camera is basically simulated HDR.
That is what a normal HDR mode is supposed to do. But then Google's HDR+ in the Nexus 5 isn't a normal HDR mode.