At its simplest biochar is any organic matter, such as wood, leaves, straw or twigs which has been heated up to the point where it 'chars' (goes black). If you have ever burnt toast you've seen this in action. Charcoal used for cooking is a form of biochar, however the term is usually reserved for when the black char is added to the ground as a soil improver.

The exact mechanisms by which fertility is improved are still being worked out, but the basic gist is that nutrients are prevented from leeching away by the porous carbon. The carbon also provides a 'home' for beneficial bacteria and fungii and help overall soil health to thrive.
The best bit from an environmental standpoint is that biochar, as opposed to compost or manure, once added to soil is permenantly stable - the carbon trapped in it is effectively removed indefinitely from the carbon cycle. Making biochar and adding it to your soil actually reduces the overall amount of Carbon Dioxide, the main gas contributing to global warming.
This is known as Carbon Sequestration and is something governments worldwide are investing huge amounts of money in. Don't they know it can be made in the backyard for free?
Not half bad for a few pounds of the black stuff! And all made from garden or agricultural wastes.
I've spent quite a bit of time learning how to make biochar to add to my own veggie patches and for me it serves a multitude of purposes. I can get rid of bulky garden wastes that are not suitable for burning in my wood stove, it improves the soil and does a little bit to offset my personal carbon footprint.
If you have time, space and stuff to burn it is well worth a shot!
This site has excellent technical information about using char, although it is targeted more at industrial scale farming applications than the home user/maker.
You can learn about How To Make Biochar
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