Charcoal is a black porous substance that although resembles coal, is made from wood and organic plant matter that has been burnt while being starved of oxygen. During this burning process to produce the charcoal any water and gas that is stuck in the wood is removed. Charcoal is one of the popular forms of fuel as it burns hotter and cleaner than many other fuels. It is also long burning and smokeless so there are no by products. It is a good fuel for cooking and smelting and is usually favoured by blacksmiths; this is due to the properties it holds when it burns. Coal is made from plant matter which has been buried and compressed over hundreds of years; this is why coal was mined because it was usually found deep under ground. When coal burns it varies in temperature and also purity, some types of coal can give off fewer or more by products than others. This is why charcoal is sill the favored fuel source.
Shop bought charcoal is not made from solid wood like natural charcoal is, it is made from compressed sawdust, but the process of making it is still the same:
The carbon rich material (sawdust, wood, organic plant matter) is dried out and subjected to extreme heat 840°F-950°F (450°C-510°C), this is done by putting the materials into a kiln, furnace or metal container where the oxygen level is very low. It is then left in the vessel until it has dried out and turned into charcoal. This process can take an extremely long time depending on how much wood or organic plant matter is being burnt, if more charcoal is being made in one go, it will take longer than if 5 bits were being made. The video below shows how people hundreds of years ago would have made charcoal without having access to metal tins and quick lighting fires as we do today.
References:
http://www.wisegeek.org/what-is-charcoal.htm
http://www.woodlands.co.uk/blog/practical-guides/how-do-you-make-charcoal/
If you go down to the woods today....... 
So WHY does charcoal burn hotter than dry wood or coal? How much hotter?
I have just got a thermometer than measures temperatures a safe distance away, so we can use it to measure temperatures of fires next time we are in the woods.
Katie:
I was just wondering, are there any types of woods that produce more or better charcoal than others?
Charcoal is effectively pure Carbon so when is burn the fire is only burning the carbon and no other waste products. Where as when wood is being burnt other things like the trapped gasses and water inside also have to be burnt off for the wood to burn. How hot the charcoal burns all depends on what it was made out of in the first place, typically charcoal can burn between 200 and 400 F but some types can burn at over 1000 F. Carcoal can be made out of many different woods, but the best seems to be any type of hardwood like oak, cherry or apple as it is a denser material and doesn’t producs as much ash and burns longer, but if you used compacted sawdust to make charcoal you would be left with alot of ash and it’s likely it would not burn as long as it would break up.