"Tannins are a class of astringent, polyphenolic biomolecules that bind to and precipitate proteins and various other organic compounds including amino acids and alkaloids." - Wikipedia
Tannin is a popular word in the wine industry and it may be a bit hard to understand at first. Red wines are generally higher in tannins than white and that's part of the reason the majority of red wines are dry instead of sweet.
Here is an easier explanation:
Have you ever peeled the skin off a grape? It has a flavor that strips the moisture from your mouth (it's dry). The reason for this is the tannins that are in the skin. Since red wines are produced with more contact with the grape skins, they absorb more of that dryness. Due to this extended time of contact with the skins, the wine is also transformed from clear to red in color.
Working as a natural antioxidant which protects the wine, tannins are a direct reason for certain red wines to be so age worthy (like Cabernet Sauvignon). They also have many health benefits!