Like all true teas, green tea comes from the Camellia sinensis plant. Green tea originated in China, but has also become increasingly popular (almost to the point of exclusivity) in Japan, and it is also grown in other major tea-producing areas like India, Sri Lanka, and South America, although the level of craftsmanship is often greatly reduced. What makes green tea differ from oolong, black, white, pu-erh, etc., is the method by which it's processed. In general, green tea is plucked then withered, steamed, and/or fired to stop the oxidization/fermentation process that would result in oolong or black tea. The different temperatures and processes the tea goes through when it's being fired or steamed, in conjunction with the tea plant varietal and the profile of the leaves selected, largely determine the flavor and character of the tea.
For Chinese green tea, the earlier the tea leaves are harvested (from as early as February through the beginning of April, depending on weather conditions), the higher-quality and more expensive they are; these teas usually consist primarily of the buds and maybe a few of the first leaves. Of course, there are exceptions to these rules--two of the most famous green teas in China--Taiping Hou Kui and Liu An Gua Pian--are produced using larger, whole leaves and no buds. In Japan, the harvesting situation is similar, with the highest prices attributed to earlier harvests. A big difference, though, is that the highest-quality Japanese teas are shade grown, and generally don't have whole-leaf appearance after processing.
To illustrate the many faces green tea can take on based on its processing and leaf profile, I've assembled several examples (click for a larger picture):
From left to right, Huang Shan Mao Feng (Yellow Mt. Fur Peak), Xin Yang Mao Jian (Xin Yang Fur Tip), Long Jing (Dragon Well), Gunpowder, Super Monkey, Gyokuro Supreme (Japanese), and Matcha (also Japanese). The porcelain cup is a Chinese tea brewing utensil called a gaiwan--more on that in a later blog entry.
For the Huang Shan Mao Feng, you can clearly see the buds of the tea plant--this tea's processing more or less retains the original appearance of the tea bud. The Xin Yang Mao Jian and the Long Jing are also both based on the tea plant's buds, but differing processing methods render the buds furry and flat, respectively. For Gunpowder, mature leaves are rolled tightly into balls--the dark, glossy surface indicates that the tea is still very fresh and still contains a great deal of the juices that make its flavor strong. The white, downy hairs on the Super Monkey are present on all tea buds--they're a good indication that the tea was harvested early. The Japanese Gyokuro is the highest quality green tea in Japan--its leaves are small, thin and very dark green from the shade-grown conditions. Matcha is a powdered Japanese tea, produced from stone-ground gyokuro and whisked to a froth for drinking. These are just a few examples--especially with Chinese green tea, the finished leaves can take on numerous shapes, sizes and textures.
To return to the original impetus for this posting (why people say they don't like green tea), it's important to remember that green tea needs to be brewed correctly to maximize its quality characteristics. Black tea and oolong drinkers are used to pouring boiling water on their tea leaves and steeping them for 4 or 5 minutes. These brewing parameters won't produce a very good cup of green tea--the tender, fresh leaves need a lower temperature (about 170º for Chinese greens and even less--around 160º for Japanese greens), and shorter steeping times will yield a much more enjoyable flavor--1-2 minutes for the first infusion of a Chinese green tea, and closer to 1 minute for Japanese teas. The bad characteristics that people sometimes associate with green tea--bitterness, astringency (that "mouth-drying" effect), and overly-strong flavor--can be avoided by gentler brewing. It's worthwhile to experiment with your brewing temperature and time to find the flavor that best suits your tastes--great green tea flavor ranges from vegetal (pea-like, bean-like, or asparagus-like, for example) to fruity to nutty to grassy (especially Japanese green tea). Often, there is as much variety to be found within the green tea genre as there is between entire tea genres, so have fun exploring!