The Demeter biodynamic standard is based on the organic rules, but goes beyond them. Not only does biodynamics avoid the use of synthetic chemicals but it includes specific regenerative practices as well as the essential biodynamic soil remedies.
The theory of biodynamics itself may seem convoluted and the jargon may be difficult, but in practice it's quite simple: these are remedies that bring the effects of carefully composted medicinal herbs to your compost and to your soil. If you feed your compost pile medicines, you are much closer to what Hippocrates said: Let food be thy my medicine, medicine be they food.
Indigenous wisdom has long placed medicinal herbs in compost piles. Why wouldn't you do the same? If the compost is a living thing, why wouldn't it need the same kinds of medicine that humans would need in the same area? But even if the compost itself doesn't need those medicinal powers, imagine feeding the roots of your lettuce things like composted chamomile, yarrow, nettles, etc. By deliberately introducing oft-neglected plants like these into our compost piles, biodynamics helps create a kind of biodiversity that is rarely attained when assembling a haphazard compost pile without such medicinal herbs.
Biodynamics helps you go beyond merely avoiding what is toxic and helps you include what is vitalizing.