Adding charcoal to concrete can do a number of very cool things:
It reduces the carbon footprint of concrete,
It can make the concrete stronger,
It makes the concrete lighter in weight (lower density),
It improves the insulating properties of the concrete.
The carbon footprint of concrete is a very real concern, but biochar concrete can been low-carbon or even negative carbon.
If biochar is added as an aggregate to concrete, it can make it stronger. One factor involves the high surface area of the biochar compared to other aggregates. Another factor involves the ability of moist biochar in the mix to improve the curing process.
Having lightweight concrete is often a plus. Some of the biochar bowls and coasters I have made have a density that is only half that of regular concrete. People are surprised when they pick one up. Part of that might be due to a psychological interpretation of concrete as being heavy (and it is, in large chunks). But biochar concrete is similar to pottery when it comes to weight/density.
Ordinary concrete has thermal properties similar to limestone (lots of thermal mass, but relatively litttle insulation). Biochar adds loft, it adds lots of small air pockets in the concrete, and that makes the biochar concrete a better insulator.