Mainly there can't be any synthetic substances (fertilizers, pesticides) or chemical salts, none should ever have been applied. Less obvious are chlorinated tap water and pH Up, which should also be avoided and high NPK plant foods in general (over 10-10-10).
Other than that the materials sourced and materials in the potting mix should be all natural; plant or animal derived, or sustainably mined, and preferably come from industry by-products. OMRI\NOP or similar certification may be helpful but just because a product isn't certified doesn't mean it can't be used. A basic suitable potting mix contains mostly sphagnum peat and\or coco coir (limed), along with compost, humus or earthworm castings and a little bit of perlite or pumice. The key is being able to learn to check ingredients for red flags, primarily substances that could be harmful to soil biota.
The soil food web includes bacteria, archaea, fungi, protozoa, and nematodes. All of these organisms are carrying out functions serving to feed, protect or otherwise provide for the plant directly or indirectly, in ways big and small. Nutrient assimilation takes place in the rhizosphere (the area immediately surrounding the roots), where the roots are secreting various substances such as carbohydrates, and amino acids collectively referred to as root exudate. The exudate attracts the microbes into the rhizosphere, where their 'waste'\metabolic products are most accessible. Some organisms in particular have more intimate and interesting relationships with the plant roots, like the symbiotic mycorrhizal fungi which infect plant roots and then seek out nutrients and water for it in exchange for simple carbohydrates.
One reason the focus of organics is on natural\non-chemical inputs is these are more likely to support and less likely to harm microbial communities. Many of the organisms in soil are sensitive to things like chemical salts (fertilizers) and pesticides. The microbes are the crucial ink between the organic matter\plant food and sustained plant nutrition\nutrient uptake. I would highly suggest researching the soil food web and soil sciences a bit to help you understand. Teaming With Microbes is a great, short book that a lot of people recommend. The USDA has a great soil sciences primer online, the wikipedia has some decent info and various universities have online articles about the biology of soil.
