It isn't "just" oak, but more specifically it will be a white oak. Oaks are typically divided into red and white; without going into a treatise on woods, the main difference as applicable to beverages is that red oak is porous, white oak is not. Take a short length of each, red oak and white oak, a little thicker than a pencil and place one end in a glass of water and blow into the other end. With the red oak, you will see a fine stream of bubbles, but none with the white. It would be useful, if you're interested in more reading, to look up articles and books on cooperage, grain properties, etc. Coopers used white oak because of it's "waterproof" properties and the fact that it was highly rot resistant. Coopers were generally divided into "wet coopers" for those that worked containers to hold liquids and "dry coopers" (somtimes called white coopers) for those that worked containers to hold flour, gun powder, hardware, etc.
There are distinct grain differences among woods, too; ring porous, such as the oaks, ash, and hickory, where you can not only see the grain/rings but feel the separations between early and late wood; and ring difuse, which include maples, cherry, hop hornbeam, etc., wherein the wood is smooth to the touch, generally no distinction between early and late wood.
Charring - well, there's a lot of theories about why the barrels were charred, originally, and I'm no expert at all on anything. But I believe that it was to preserve the wood (because it would be holding a liquid) and at the same time act as a purifier/filter (charcoal takes out loads of impurities). There were pleasant unintended results, so it went from a necessity to almost an art form. Just my two-cents.
As for aging, I know of some distillers that take their product, insert oak chips (toasted or not), and put it in the freezer for a day, then take it out for a day, then repeat the process. Each in-out is a cycle that is supposed to represent a year of aging; the theory is that temperature has the effect of drawing the liquid into the wood when it's warm and driving it out when it's cold, therefore giving them the equivalent of 12-year-old bourbon (or whatever) after 24 days. Theory or not, the result is an almost perfect duplication! But, that's not something for wine or beer...
As for other woods, doesn't a particular brewery still brag about their beer being "beechwood aged?"
There's a lot more to it than this, to be sure; again, more reading from other diverse interests is a big help in understanding. As far as which woods are best, read up on smoking meats and sausages. Hardwoods = good, softwoods = gross!
Anyways, fwiw.