according to the Maya f1 help files....
Hardware rendering is...
An interactive rendering method that uses the capabilities of a computer’s graphics card to create lighting and texturing effects.
Software rendering is....
A rendering method that uses software to create lighting and texturing effects. Software rendering may take longer than hardware rendering, but is required for certain kinds of details and effects.
Essentially you will only get a very basic render with the hardware render, not dis-similar the view you have in the work area under High Quality Rendering mode. Software render uses either the built in Maya render or 3rd party renderers (Mentalray, Maxwell etc.) which means that you will get raytracing, refractions, FG, IBL all of the fancy stuff that makes an image look good.
Hope that clears things up a bit for you,