Under the strictest rabbinical supervision
The word kosher or Kasher / כָּשֵׁר, using contemporary Hebrew pronunciation, means proper, qualified, legitimate or fit for consumption. It is not unusual to characterize various objects, people and events as kosher – kosher kitchen, kosher witness, kosher business, kosher wedding and even kosher funeral.
Most commonly kosher is associated with kosher food, i.e., food that conforms to the Jewish dietary laws. Consequently, a kosher caterer is the one, who serves kosher food. This is not the same as a "kosher-style" caterer – frequently a euphemism for a non-kosher Jewish caterer or restaurant. The Torah does not specify any reason for its dietary laws. Refraining from eating non-kosher food is one of the biblical commandments and for an observant Jew there is no need for any other reason.
Kosher is clean. Food products of animal origin, including meat, milk and eggs, are kosher only when they come from those species that the Torah classifies as clean. Cud-chewing animals (מעלת גרה), whose hooves are completely split (מפרסת פרסה ושסעת שׁסע), are clean. Some of the clean animals, both of the signs that distinguish them and all the animals, which have only one of the kosher signs and, therefore, unclean, are listed in the Books of Leviticus 11:2-11:7 and Deuteronomy 14:4-14:8.
The Torah does not specify characteristics of clean birds. It enumerates, instead, 24 families of unclean fowl (Leviticus 11:13-11:19 and Deuteronomy 14:12-14:19) implying that all others are clean. However, in the course of the centuries the exact identities of unclean birds became doubtful. The Mishnah in Tractate Chullin 3:22–23 describes four signs of kosher birds, but in practice neither the signs of the kosher fowl nor the signs of kosher animals are relied upon in absence of an established tradition.
Fish must have fins (סנפיר) and scales (קשקשת) to be kosher (Leviticus 11:9-11:12 and Deuteronomy 14:9-14:10). The scales must be easily removable without damaging the skin. In fact, the presence of scales is both necessary and sufficient evidence that the fish is kosher. Therefore, ground fish or fillet that does not have a skin tab with scales attached to the flesh is deemed to be not kosher, unless its preparation was properly supervised. All other creatures, including shellfish, rodents, reptiles and insects are not kosher, except for certain species of locust (Leviticus 11:10, 11:20-11:23, 11:29-11:30, 11:42-11:43 and Deuteronomy 14:19).
Something that is not kosher is called treif / טרײף. It is derived from Trefah / טרפהה – mauled or torn, in Hebrew, since the meat of an animal or a bird that was not ritually slaughtered (e.g., was mauled, torn, shot or died of natural causes) is the primary example of non-kosher food, as it is written in the Torah “you will slaughter from your cattle and from your flock, which the Lord has given you, as I have commanded you / וזבחת מבקרך ומצאנך אשר נתן ה' לך כאשר צויתך” (Deuteronomy 12:21), and “do not eat any flesh that was torn in the field / ובשר בשּׂדה טרפה לא תאכלו” (Exodus 22:30) and “do not eat any carrion / לא תאכלו כל נבלה” (Deuteronomy 14:21). It is forbidden to eat limbs of a living animal - עבר מן החי, or its blood, as it is written “But flesh with its soul, its blood do not eat / אך בשר בנפשו דמו לא תאכלו” (Genesis 9:4). Fish does not have to be ritually slaughtered prior to eating (based on Numbers 11:22), but may not be eaten while it is still alive either.
Glatt kosher. According to Jewish tradition, a life threatening injury, illness or disorder also renders an animal to be traif. There are eight types of defects that make the animal unfit to be eaten. One area that is most prone to defects – the lungs – must be carefully examined. If the lungs of a kosher animal are smooth (Glatt / גלאַט in Yiddish, Chalack / חלק in Hebrew) and free of any possible lesions and adhesions, the meat is considered to be glatt kosher. Otherwise, the meat might still be strictly kosher, but not glatt kosher, since the doubts had to be resolved by a competent rabbi. Nowadays, glatt kosher is applied not only to meat but to other kosher foods as well in order to emphasize that the food is prepared according to the highest standards and is unquestionably kosher.