Wines made from certain grapes — chardonnay, semillon, the Bordeaux reds and so on — gain complexity and add layers of flavor when aged in new oak barrels. However, the type of barrel and the time in barrel can vary infinitely explains this Seattle Times article.
Oak may be sourced from various forests in Europe and America, and once harvested, may be air-dried or kiln-dried, aged for different lengths of time and then toasted to different degrees. Winemakers love to play with the wide range of flavors available to them, which they often compare to a chef’s spice rack. This is all well and good, but the final results, as always, depend upon the skill of the artist.
Neutral oak is wood that has been used for more than two or three years. After that the barrel has been drained of flavors and is simply an aerobic medium for wine fermentation and storage. Apart from barrels, there are many types of oak flavoring available to wineries that do not wish to pay the $1,000 or so that good new barrels will cost. Oak staves, chips, powders, etc., can add certain flavors (especially vanilla) to cheap wines, but nothing comes close to the complexity gained by aging fine wine in great barrels.
American oak is generally spicy, sometimes offering pickled notes, while French oak is toasty and more subtle.