*Less harsh chemicals. Although technically speaking, everything in our beauty cabinet contains chemicals, some are harsher than others. An especially irritating chemical component is sodium lauryl sulfate (SLS), common in most beauty products. This is why so many natural products are now "sulfate-free," so check the labels.
*Less fragrances and artificial colorants. In reality, your lavender-scented body wash is only purple because of chemical dyes. And that strongly-scented body butter probably contains synthetic fragrances. Both can cause skin irritations, which is why many natural beauty products will be lightly colored with only a slight scent (oftentimes from essential oils).
*Fewer preservatives. While preservatives are necessary to prevent products from spoiling, some can be irritating to the skin, especially if your skin is already dry or you suffer from a condition like eczema. Parabens, which are found in most beauty products, have even been linked to breast cancer--although there haven't yet been any conclusive studies on the correlation.
When choosing between natural brands, make sure to do your homework; many brands now use the words "natural" or "organic" as selling points in order to charge more for their products. Be sure to read the labels and be sure that your product doesn't contain irritating ingredients; if you're looking for products free from sulfates or fragrances, for example, don't assume that a product will be free from these things just because its natural.