Like all aspects of Jewish life what is and is not allowed when it comes to food is determined by the Torah and the Talmud. From the beginning, God set down the laws of kashrut. These laws are found in the Torah. Further explanations of the laws can be found in the Talmud.
There are foods which are considered unclean like pork and all shellfish, there are foods that are not allowed with others like mixing meat and dairy, and there are foods not allowed at certain times of the year like during Pesach. And then there are the foods which are considered clean and the people are allowed to eat.
Three categories of Jewish Dishes
Those dishes that are deemed as clean come in three categories; fleische (meat), milcha (dairy), and parve (neutral).
Fleische dishes include beef, chicken, and lamb. Certain wildlife like deer and some birds are also allowed. When serving dishes with these ingredients they must not contain or be served with any dairy items.
Milcha dishes include any item that uses a milk product which is of curse milk, butter, and cream. The Torah states that milk or dairy products cannot be used with meat that is why there must not only be a separation of the dishes but a time span between the two. The exact time limit varies from Rabbi to Rabbi but it includes a number of hours.
Parve dishes include neither meat or dairy. Things like rice or potatoes before adding the butter or cream, bread made without milk, vegetables, and fish.
Some Jews choose to lean more toward being a vegetarian in order to avoid the meat/dairy issue. Not only are these things not mixed they even require a separate set of dishes for each.
Every ethnic group has foods that are affiliated with that particular group and the Jews are no exception. Mention Jewish food and many people will say knishes, bagels with or without lox, matzo balls and matzo ball soup, latkas, and kugel.
During Pesach (Passover) Jews do not eat leavened bread. Matzo meal is used instead. From the matzo meal comes matzos and matzo balls. Kugel is similar to a square pie only it is made with noodles or potatoes. Knishes are made with potatoes as are latkas (potato pancakes).
Food marked with the proper kosher symbol known as a heksher have been prepared according to the laws of kashrut and approved by a Rabbi. Kosher foods made at home also follow the laws of kashrut but the Rabbi is usually not present to supervise the affair.