A wine's color gives many clues to its character. First, color reflects the specific variety of grape (or grapes) the wine is made from. Take two common red grapes, Cabernet Sauvignon and Pinot Noir. Cabernet berries are typically smaller, with thicker, darker skins, than Pinot Noir. As a result, wines based on Cabernet tend to show darker colors, leaning toward purple and black, instead of the ruby tones associated with Pinot.
Second, color is influenced by growing conditions in the vineyard. A warm summer and dry autumn produce grapes that are fully ripe, with a high ratio of skin to juice, resulting in dark colors. A cool summer or a rainy harvest can result in unripe or diluted grapes, which will show up in colors with lighter hues and less intensity.
Vinification techniques can also affect color. When red wines ferment, the grape skins are left to macerate in the juice, like a tea bag steeping in warm water. The elements that create color, the anthocyanins, are found in the skins, not the juice itself (most grapes, even red varieties, have clear juice), so the longer the skins steep, the darker the color will be.
Even after fermentation is over and the skins are discarded, some solid material remain in suspension in the wine. Some wine makers choose to remove this material, through fining or filtering; others believe the wine benefits from a little residual deposit.
Time in bottle -- the inevitable process of aging -- also has an impact. Young red wines are full of anthocyanins, and so their colors are deeper; with maturity, these coloring elements evolve, lightening through red to colors described as "brick" or "amber," slowly combining and falling out of suspension in the wine, creating a sediment in the bottom of the bottle.
So if you pour a glass of red wine and look at it closely, you may find a deep garnet color, with good intensity but not brilliantly clear. You might reasonably infer that the wine is made from Cabernet Sauvignon grown in a warm climate, that the wine maker chose to filter only lightly, and that it's from a recent good vintage.
If the tastings not blind and you already know what the wine is, you can compare its color with what you might expect: Perhaps it's exceptionally dark for a week to age, indicating good grape-growing or wine making abilities, or maybe it's already faded for its age, suggesting that the grapes lacked concentration or the winemaker was unable to extract the intensity.