Carbon bonded to other carbon, which is a kind of reduced carbon, is what we use for energy. What kind of energy you ask? Well, how about food, which is a kind of reduced carbon. Food is sugars, proteins, fats, etc, which are all carbon chains. Also how about fossil fuels like gasoline (let’s call that octane). The bonds between the carbons have energy in them, and we get that energy out by digesting them or burning them.
Other carbon chains you might like: animals (which you eat), plants (which you eat), you, everyone you know, fossil fuels (which you burn), most polymers like plastic bags, soda bottles, and on and on and on.
The Clear Science staff is kind of over-simplifying here: there are other elements in these molecular chains, like H, O, and N. But anything organic is based on carbon chains, so you can think of them as being reduced carbon.