This question is a bit divisive since opinions on the subject are varied and strongly held. The Wikipedia definition, which is a good jumping-off point, describes natural winemaking as “minimal chemical and technological intervention in growing grapes and making them into wine.”
Strictly speaking, wine is not natural. Wine does not just happen — it is the result of work, decisions and manipulation by people to craft a beverage in a certain style. Even if some ripe grapes did somehow fall into a container, crush themselves and ferment to create the blend of alcohol, water and other minor (by volume) ingredients that we call wine, almost nobody would recognize the result as wine. And, it would spoil almost immediately.
So, natural wine is not black and white — it’s a question of how much manipulation you consider desirable or acceptable. Fundamentally, from speaking to natural winemakers it becomes clear that natural winemaking is really a philosophy of making wine more in the vines than in the cellar. The idea is to grow healthy grapes and let the resulting wine be shaped by the juice that goes into it as opposed to post-manipulation — adding sulfites, strong wood flavors through intensive use of oak barrels, lots of blending, coloring and artificial additives, and the like. The thinking is that this produces a wider variety of more interesting wines that express their place of origin more than conventional wines. If this is true is matter of opinion.
In my opinion, the problem with the “natural” label is that it penalizes a lot of exceptional winemakers who do not adhere so strictly to this philosophy, which in certain circles is almost a religion. Many careful, thoughtful winemakers make the decision to use commercially-isolated yeasts (as opposed to “wild” yeasts favored in natural winemaking) and judicious amounts of sulfites (to protect the wine from bacteria and oxidation, and to help it maintain the purity of its flavor while in bottle). Personally, I would argue that these decisions do not reduce the quality or inherent value of the wine — in fact they often increase it, depending on your definition of quality.