Kosher food is food that meets Jewish dietary laws, or kashrut. The word kashrut comes from a Hebrew word for "fit" or "proper." Though many unfamiliar with the concept assume "kosher food" is "healthy food," it actually refers to any food that has been prepared in adherence to Jewish law, or halacha. Conversely, foods labeled as "Jewish" aren't necessarily kosher. Kreplach, cholent, kugel, latke, and kishka are all traditionally Jewish foods, but if they are not prepared in accordance with kashrut, they will not be kosher.
Kashrut has a rather extensive set of laws. There are laws derived directly from the Torah or bible (d'orita) which generally have greater importance and others that have been identified over the years by Rabbis (d'rabanan) because there may be some unclear aspects by the biblical law alone. Moreover, there is a lot of dispute over the nuance of kashrut. As a result, what one segment of the Jewish community deems as kosher may not jive with that of another segment. There are, however, many agreed upon general rules.
Prohibited Animals
A good portion of kosher food regulations, and perhaps the laws that are some of the most well known among non-Jews, has to do with particular animals that cannot be consumed — pig probably being the most well known. According to the Torah, cloven hoofed, cud-chewing mammals can be kosher. Cows, deer, sheep and goats, for example, may be kosher, while pigs and rabbits, for example, never are. Only certain birds may be considered kosher in the United States, including chicken, duck, goose, and turkey. For seafood or fish to be kosher, it must have fins and easily removable scales, like tuna, carp and herring. Shellfish generally, and lobsters, shrimp and clams specifically, are not kosher.
Kosher Slaughter
Kashrut has very extensive laws on the proper slaughter of animals as well. So, while a particular animal, like a cow, may be kosher, if it is not properly slaughtered, it is not kosher. Both poultry and meat must be slaughtered under strict dietary guidelines called shechita. These rules of slaughter require, among other things, that (1) only trained butchers shochet) perform the slaughter, (2) the animal not have any medical defect like a disease, (3) the animal be killed with a sharp knife and one swift motion to the carotid artery, and (4) as much blood is removed as possible through a process known as kashering.
The Separation of Dairy and Meat
Milk and meat cannot be eaten or served together. In fact, many observant restaurants are exclusively dairy (milchig) or meat (fleishig) to ensure that there is no cross-contamination in observing this aspect of kashrut. Pareve food — food that is neither meat nor dairy, such as vegetables, eggs, fish, and grains — can typically be served and eaten with either meat or dairy foods. Rabbinic law includes poultry in this prohibition so fried chicken that has been breaded with a milk-based batter isn't kosher, but because fish is pareve, milk-battered and fried fish or bagels with lox and cream cheese is kosher.
Kosher Kitchens
Kosher kitchens must maintain separate sets of utensils, pots, pans, dishes, and anything else that comes in contact with food for using with milk and meat. In addition, dishes and utensils in a kosher kitchen can't be washed together. If a kitchen has two sinks or dishwashers, it is an ideal setup for a kosher family; if not, separate wash buckets are often used. Dishes and utensils must be dried using separate racks or dishtowels as well.
Product Labeling
There are many other rules to be followed for anything to be considered kosher food. To make identification easier on the consumer, kosher food is often identified as such by its kashrut certification on the food's package. Kashrut certification is generally indicated by an identifiable symbol (hechsher) or by the word pareve. In order to get that certification, an authorized Rabbi must supervise the process the food underwent. Because different denominations apply different nuanced interpretations of kashrut, there are actually many different types of symbols based on the kosher certifying agency. The Union of Orthodox Congregations is a common certifying agency in the US whose symbol is the letter "U" inside of a circle.
The Word "Kosher" in American English
Though the formal use of the Hebrew/Yiddish word "kosher" technically only refers to food that is "ritually fit or pure," it has come to be commonly but informally used in American English to refer to most anything, food or otherwise, that is appropriate, legitimate, proper, or genuine. Instead of saying "that's not right," one might say "that's not kosher."