Terra Preta is dark soil that was created when ancient Amazonians disposed of waste by slow burning. While it was not created with an aim to help crop production, the soil is extremely fertile. Modern farmers are reaping the benefits.
Biochar is the modern application of the ancient methodology called slash and char. Biochar captures airborne carbon and stores it in the ground, thus reducing greenhouse gases. Methane and nitrous oxide soil emissions are dampened as well. Not to be confused with slash-and-burn, where farmers release greenhouse gases when they prepare fields by cutting and burning, slash-and-char depends on a low-heat smoldering burn. It also occurs after naturally-occurring fires as they slowly burn out.
The excellent video above explains biochar in great detail.