Tannins are a natural component of the grape skins, seeds and stems. The scientific word for these component is polyphenols. Polyphenols released from the skins, seeds and stems will soak in the grape juice just after the grapes have been pressed and are what give certain wines, such as Cabernet Sauvignon, their characteristic dryness or astringency. The effect of tannins in the wine creates a drying sensation in your mouth when you drink it. Depending on how dry your mouth feels, you can determine whether a wine is high or low in tannins. A wine that is high in tannins is called tannic.
The longer the skins, seeds and stems soak in the juice, the more tannin content the wine acquires. This explains why red wines have stronger tannins than white wines, since the production of a red wine requires that the skins stays with the juice in order to impart more color to the wine, thereby adding more tannins to the juice. Further, by extracting the characteristics of tannins, they are able to add deeper complexity to the wine.
Winemakers actually love tannins, because they work as a natural antioxidant to protect the wine. This is actually a key reason why certain red wines, including Cabernet Sauvignon, can be so aged without going bad. And, as we know, antioxidants are not just useful for helping age the wine, they also have great health benefits in humans.
The only downside to tannins is that they may give some people headaches. A good way to test if you are susceptible to headaches from tannin, is to determine whether or not similar substances that are strong in tannins, such as dark chocolate and strong black tea, produce the same effect. Tannin headaches are rare, usually we just get a wine headache from consuming too much, but if you do realize you suffer from them, sticking to white wine, which is very low in tannins, would solve your tannin headaches.