LEMON
Lemon is a citrus fruit, along orange, grapefruit, lime, and mandarine. They all originate from Asia and nowadays, through extensive trading, they are grown in many mild and warm climates around the world. Citrus fruits are interesting in that they contain not only the aromatic acidic flesh but also have a good amount of aromatic oils in their skin, which is therefore often used for enhancing flavors in dishes (lemon zest, orange zest). Another good quality of citrus fruits is their relatively long storage time, partially due to this tough skin that protects them from microbes and mechanical damage.
Lemons are actually, or probably, a cross between an older kind of fruit called citron and a common one - lime. They may actually have been crossed in two steps, and got their final shape about 2000 years ago.
The main use of lemon in cooking is due to its acidity and freshness. Not only dishes can be refreshed and acidified with lemons, also drinks and sodas are. Lemons can also be briefly cooked in sugar syrup and stored for a longer time in a refrigerator, and served as a confit that complements a dish. It is also great for preventing oxidation of other fruits, e.g. apples, and also artichokes. If they are briefly dipped in lemon juice, they will be prevented from becoming brown.
Nutritionally speaking, sure you don't really eat lemons as they are, but still they contribute some important health molecules to your body even in lesser amounts. Vitamin C is an obvious one - about 100 g lemon covers your daily need for this vitamin that is important for its antioxidant activity and for producing collagen - the major protein in our bodies. Another molecule called limonin is also present in lemons, and it's also an antioxidant - a very powerful one that battles against cancerous changes in our cells. Vitamin C and possibly also limonin are also good to prevent arthritis.
When you buy lemons, pick up the ones with thinner skins as these are the specimens that have developed the most juicy flesh. The color should be yellow of course, as the ones with some green lines are not yet fully ripened and will be more acidic. The lemons you probably want are more sweet and that's what you will get if you follow this advice.
You can keep lemons at room temperature for a couple of weeks, as long as you keep them away from the sun. If you want to store lemon juice or zest, they have a shorter lifespan, maybe a few days, but the best thing of course is to use juice and zest fresh - this is where most lemony flavor is apparent.
Lemon is a good partner for chocolate (!) and many acidic fruits like raspberries, black currants, strawberries, grapefruits, or oranges. Of course it should be used in moderate amounts unless you want to make it a dominating flavor. It can also be served with lime and honey, and enhanced by cardamom. Otherwise, its main use in cooking is to get that extra sting to some dishes, like fish or shellfish, some sauces, or just to add some acidity to a certain dish.