Kosher ... it is a dietary custom which respects humane treatment of animals including how they are raised and how they are slaughtered. It also forbids eating the milk or eggs they give us, along side of the sacrificed life they give us for consumption. Due to illnesses caused in the past from pigs and shellfish, such are excluded entirely from a kosher diet.
This is not exactly true.
Certain types of meat are forbidden by divine fiat. These are listed in Leviticus, Chapter 11, and it's basically pork and other critters that don't have cloven hoofs and chew their cud, poultry for which the Jews don't have a tradition of eating, and seafood that doesn't have scales and fins. For practical purposes what's permitted is beef, veal, lamb, goat, venison, bison, chicken, turkey, pigeons, some kinds of duck, goose, and finfish with scales. (Catfish is a no-no.) Milk and eggs from forbidden animals are also forbidden. The only exception is honey.
Meat has to be specifically slaughtered for eating, so road kill or an animal that dies on its own is not permitted.
The rabbis in the days of the Talmud added more stuff:
The meat has to be slaughtered in a specific manner. This manner is thought to be more humane than the way people used to slaughter meat, but not everyone agrees that this is true. As far as I know, there are no rules about how the animal is raised, as long as it is a permitted animal.
The meat has to be inspected to see if there are signs that the animal wasn't healthy and might have died on its own, thus making it the equivalent of road kill, and thus not kosher. These signs were codified about 1,500-2,000 years ago and might not correlate with modern veterinary knowledge. Meat that doesn't pass this inspection is still perfectly safe to eat, and is commonly sold to the non-kosher market.
Meat (including poultry) cannot be mixed with, cooked with, or eaten together with milk or any products derived from milk. However eggs and fish can be eaten with either meat or dairy. (Some Orthodox Jews don't eat meat and fish together because a religious law code from the 16th century claimed that doing so was unhealthy.) Eggs and fish (and all vegetables) are what is known as "pareve."
Meat and dairy products need to be cooked, served and eaten on separate utensils. Thus, if someone is really strict about keeping kosher (and certainly a caterer like Boorenstein is), they will have at least two complete sets of dishes, eating utensils, and cooking utensils, one for meals containing meat (including poultry) and one for meals with dairy products. They might even have a third set that's pareve for making salads and such.
There are a few other fine points that I've omitted, but these are the basics.
The religious reason for doing all of this is strictly because "God said so." More modern rabbis have added various ritual or spiritual benefits that might derive observing these taboos. It certainly helps reinforce group identity of a minority people that might be in danger of disappearing through assimilation. I believe that few scholars now believe that these were selected for health reasons. Even back in the Bronze age, people knew that thorough cooking of pork prevented trichinosis, so there's really no health benefit to avoiding pork.
I think the selection of permitted animals comes a lot from the fact that the Jews are descended from nomadic herders from the hill country, and sheep, goat, and cattle were their customary foods. I'm not sure where the ban on mixing meat and milk comes from, aside from being an interpretation of a biblical verse banning cooking a kid in its mother's milk. Some of these may have been pagan practices that the Rabbis wanted kept out of the Jewish religion. The business about the utensils comes from the days when bowls, plates, pots, etc. were commonly made of wood or unglazed pottery, so they might retain some of the food or the flavor of the food previously cooked or served in them, so in order to keep the foods separate, you had to keep the dishes separate..
All of this is pretty complicated. Fortunately, when ordering a kosher meal on Amtrak, the person eating the food doesn't have to worry about the details.