Wikipedia has this definition: "(lo-fi photography) refers to unconventional photographic practices, chosen for aesthetics, which to give an impression of low quality. Popular techniques include the use of toy cameras or pinhole cameras for their distinctive stylistic effects."
In today's context, it refers to the use of effects ("FX") in mobile phone apps like Instagram, Pixlr-o-matic, etc., to create the old look. This article in dpreview gives a good introduction to what lo-fi photography is all about: http://www.dpreview.com/articles/9771282693/digital-lo-fi-photography-part-1 . Some of the effects have found their way from smartphones into conventional cameras, albeit the lower entry-level ones.
My thoughts on this:
Even an amateur or a professional photographer can engage in lo-fi photography. It is not about the person, it is more to do with the practice of how the photo is taken, processed, and published. The thrill of lo-fi photography is the unexpectedness of it. After a picture is casually taken, one filter after another is applied to it. Then an unexpectedly eye-catching image appears, giving him the adrenalin rush. The image is immediately shared on a social website.
Incidentally, lo-fi photos are often published alongside other photos casually shot with the smartphone but not modified with effects.
Whether lo-fi will eventually emerge as an established genre in its own right remains to be seen, but I seriously doubt it. I think it will always be a loose aggregation of ad hoc point-and-shoot work with no direct commercial value. The good ones are like well-drawn graffitis (no negative connotation intended). The bad ones are simply kitsch.
An amateur and a professional photographer takes years to hone the craft of photography. A lot of effort and costs go into setting up a shot. Equipment is top notch, or at least they get increasingly more sophisticated as he ascends the learning curve. In fact, his shots are often post-processed to give it a less-than natural look. In that sense, it is akin to lo-fi photography but the difference immediately stops there.