HDR stands for High Dynamic Range - an overly simple explanation is that you get detail in the shadows and highlights. (For a more complete understanding of HDR check out "Modern HDR photography, a how-to or Saturday morning relaxation" on a blog called Memoirs On A Rainy Day.)
With the iPhone, we can create a sort of faux HDR effect to recover detail in highlighted area (provided there is some info there to recover) and we can add fill light in our shadow areas (again provided there is some info there.)
Here's a shot near Baldwin Beach at Lake Tahoe one evening. Notice how the foreground is dark, without much detail. The iPhone exposed for the sky.
I used the Photoforge app which has an HDR setting that allows you sliders to open shadows and recover highlights. It's okay, but no matter how I move the sliders, it ends up being low contrast. That can be good in some cases, but I want a little more drama in this scene.
Here I use the iFlashReady app to open up the shadows - it has 3 flash fill settings and only works on adding light to the dark. Voila! Now it has the kind of drama I'm looking for. This is my favorite faux HDR tool so far.