Kashrut refers to Jewish dietary laws. Food in accord with halakha (Jewish law) is termed kosher in English, from the Hebrew term kashér, meaning "fit" (in this context, fit for consumption by Jews according to traditional Jewish law). Food that is not in accord with Jewish law is called treif. Treif meat is meat from a non-kosher animal or a kosher animal that has not been properly slaughtered according to Jewish law.
Many of the basic laws of kashrut are in the Torah's Book of Leviticus, with their details set down in the oral law (the Mishnah and the Talmud). Many varied reasons have been offered for these laws, ranging from philosophical and ritualistic, to practical and hygienic.
By extension, the word kosher means legitimate, acceptable, permissible, genuine or authentic, in a broader sense.
The Islamic equivalent for Muslims is halal, which overlaps with kosher, but is not identical.
Examples of kashrut principles:
Only meat from particular species is permissible:
Only mammals that chew their cud (ruminate) and have cloven hooves are kosher. Birds must fit certain criteria; birds of prey are not kosher. There must be an established tradition that a bird is kosher before it can be consumed. Fish must have fins and scales to be kosher. Shellfish and non-fish water fauna are not kosher. Insects are not kosher, except for certain species of kosher locust (unrecognized in most communities).
Meat and milk (or derivatives) cannot be mixed, i.e. meat and dairy products are not served at the same meal, served or cooked in the same utensils, or stored together. Observant Jews have separate sets of dishes for meat and milk.
* Info courtesy of Wikipedia