Even chemists don't fully understand the aging process of wine. I agree with the comments of the previous posters, but I just thought I'd throw in my two cents as well.
In addition to tannins softening and oak integrating, primary fruit flavours will generally give way to secondary and tertiary flavours (ie. wine will become less fruity and give rise to more complexity and often to earthy, nutty, leathery notes.) This is important to keep in mind for wines that are meant to be drunk while fresh and fruity (eg. rose, Moscato, Gamay, etc.). These styles of wine might benefit from a few months of bottle age in order to integrate and overcome any bottle shock, but should not be aged too long, or they'll lose their chief attribute.
Aging is essential for some wines to reach their peak and it's always interesting to squirrel a couple bottles away for a few years to see what happens with them; but don't be mistaken into believing that age is going to improve all wines... some are best fruity and young. A general rule is that the higher the level of tannin, acidity and overall extract, the more aging potential the wine will have.