“Keeping kosher” means eating in accordance with the Biblical and Rabbinical laws. This includes refraining from eating animals, which do not chew the cud and have completely cloven hooves, such as a pig, horse, dog or cat, or products therefrom. Seafood is not kosher, apart from fish with fins and scales. Fruits, vegetables, nuts and grains are kosher.
Additionally, meat from a listed kosher animal, such as a cow, goat or sheep, or birds such as a chicken, duck or turkey, must undergo slaughter (shechitah) in accordance with the Jewish Law and then be rendered kosher by soaking and salting, again, in accordance with the Jewish Law.
Insects, reptiles, carnivorous mammals and birds of prey, are, thank G-d, not kosher.
Additionally, Jews are prohibited from eating kosher animal milk products (from cows and goats, for example), together with kosher meat products.
Cheeses need to be supervised kosher to ensure that the rennet is kosher and thus the cheese is too.
Rabbinical supervision is required on all meat, wine and many other food and beverage products. Depending on one’s custom, the national or local rabbinical supervision may suffice. Some Jews require the meat to be “without-a-doubt” (Glatt) or require specific high-level kosher certification (sometimes known as Mehadrin, Bedatz or Kedassia) and order “special kosher” meals on flights.
Most orthodox Jews will not drink wine, milk, bread or baked products without a kosher certification or being on a certified kosher list.
Local laws often allow ingredients which are less than two percent of a food product not to be listed. For example, in England, some ice creams, cakes, cookies and bread products are made with lard (pig fat) and are thus not kosher. They therefore need supervision on two counts: a) to ensure that all the contents are kosher and for bread b) to ensure that they were baked by/in the presence of a Jew and meet the Rabbinical Law requirements.
Certain food additives (E numbers) are derived from insects and worms and render food/beverage products non-kosher, such as cochineal (E120). A list of non vegetarian E numbers can be found at: http://www.veggieglobal.com/nutrition/non-vegetarian-food-additives.htm
It is permissible (and required, if no kosher alternative is available) to save lives and provide non-kosher food/beverage/drugs to a sick/starved person to save/promote their life, since the value of life exceeds the prohibition of keeping kosher.
On Passover (Pesach), Jews are forbidden to eat leaven bread, leaven bread being defined as having taken more than eighteen minutes to prepare and bake. Jews are further required to eat unleaven bread (Matzah) on Passover. Furthermore, any products containing flour of the five major grains (wheat, barley, spelt, oats and rye) are not permissible on Passover, apart from Matzah, Matzah meal and Matzah meal products. Thus, on Passover, there is an extra requirement for purchasing foods with a “Kosher for Passover” certification or stamp. Tradition amongst the European Jews (Ashkenazi Jews) extended this to refraining from products which appear as grain (including corn, legumes, beans and pulses and products therefrom).
Once, keeping kosher was complex and limited most Jews to places where there was a Rabbi, a Jewish ritual slaughterer (shochet) and large population of Jews. Today, in the information age, you just need a bit of good will and list of links to show you the way. As it says on the back of, almost, your favorite currency “In G-d, we trust”.