Chemical
Biochar is awesome. It works similar to the activated
carbon that filters use.
It absorbs all the awesome minerals in the soil but doesn't hold on to it too tightly so the plants can still get to it.
Because the plants have to do less work to get the minerals they need they use less water.
Biological
Biochar also has an increase surface area allow more healthy life living microbe to co-exist per cubic feet of soil.
This means bad microbes are out-competed, and with more space/resource even the bad ones don't feel the need to invade a tree just to survive
Physical
Biochar is mostly air and it will make your soil more porous, allow more air into soil and more water storage.
Electrical
Other than lead acid battery, every other type uses activated carbon(biochar) anode to get electron to do work.
There is a reason why and we are just utilizing it's natural properties
THE BAD.
Similar to how mixing sawdust into the soil, will end up with all the nitrogen/minerals being locked up in the microbial explosion and the trees/plants will suffer until they use up all the sawdust and then die returning all the mineral/nitrogen to soil. Biochar will do something similar, it will enable a microbial explosion which will create a similar situation. This is why alot of folks add it to a composting system or at the very least add it to manure. I also think that unless some type of micro-minerals(rock dust) the extra mineral that the biochar is store will have to come from the surrounding soil, hopefully from the subsoil via fungi.