Tannins in wine are antioxidants. They serve to help protect wine against oxygen by binding with it, then settling out of the wine as sediment.
In other words, over time, and because of this micro-oxidation, the tannins are reduced in your wine. This will tend to make your wine taste less sharp and bitter, and more smooth and well rounded.
This is the very basis for why many French wines are not ready to drink for sometimes 10 years (or more) and why after all that time, they (in some peoples' opinions at least) become extraordinary wines.
The longer a wine can age before it starts deteriorating, the better. Or, the longer one can protect the wine from oxidation and such, the further the wine will mature before it starts to fade. The idea is wine can continue to get better and better until external factors begin to destroy the wine.
One thing that can extend the possible aging time is tannins, because they protect the wine very well. So, if along with extraordinary sanitary conditions, one can introduce enough tannins to protect the wine for a much longer time, in the end, in many case one will end up with a much better wine... if one has the patience to wait ten or more years. Of course the presence of huge amounts of tannins will tend to discourage one from drinking such a wine too early.
Even the tannins themselves, as they mellow over time, will enhance the wine considerably.
Such wines, even whites, are fermented on some portion of the stems and seeds in order to extract their tannins. By the time the wine is racked off these, the tannin level is very high; much too high to drink the wine early. This, in turn protects the wine for a longer period of time, so the wine can develop.
This is one of the complaints the French had concerning the Paris competition of 1976. Supposedly, the French wines chosen were only a few years old and would (possibly) have developed into much better wine, had they been aged out. The American wines were at their peak being only a few years old; the French wines were considered very young, being less than 8 to 10 years old. That may or may not have been a solid argument, but IMO, the French do have a point.
This affect, which tannins have, is the reason I tell people that if they add tannin powder to their wines, they will need to age them longer. Longer, yes, but very likely they also will end up being a better wine.