The Torah only allows us to eat animals that have split hooves and also chew the cud. Animals that chew the cud but do not have split hooves or vice versa may not be eaten.

What is the relevance of these physical signs to the issue of eating the animal that has or doesn't have these signs? Are these just CHUKIM (statutes) from G-D which we must obey without understanding the reason?

The Sefer Kol Bo explains the significance of these Kosher signs. The reason why certain animals chew the cud is because these types of animals feed on vegetation. And it is not in their interest to chew their food properly and slowly in one certain place. This would make them vulnerable to predators that wait to pounce on them and eat them, or to the elements, the blazing sun or driving rain. Thus, by biting off their food and swallowing it immediately, they are able to eat quickly and run for safety. This is a great benefit for these vulnerable animals. Later on, when these animals come to safer ground or more comfortable surroundings, the food comes back up from their stomachs, they grind it and then digest it properly. Therefore, "chewing the cud" is a safety mechanism for these types of animals against predators and the hostile elements.

And the reason why kosher animals also have spilt hooves and not sharp, strong claws, is because their feet serve as accessories for them to stand and walk, unlike predators, which require claws to rip apart their prey. Additionally, their split hooves enable them to flee from predators and afford them good grip even on mountainous terrain. Thus, these animals can run and jump when escaping any threat. G-D in His love for His People, requires us to abstain from eating all predatory animals. When food is digested by a person it becomes a part of him, and his nature becomes similar to that of which he ate. Thus, G-D does not want us to derive our nourishment from animals that have predatory character traits. G-D does not want us to be affected by the traits of animals that hunt and kill.

G-D only allows us to eat and absorb into our bodies those animals which survive without killing other animals. These Kosher animals, which are pursued but are not pursuers, inject into us the positive trait of non-aggression.

The Torah teaches that you are what you eat. Thus, in order to ensure that our spiritual sensitivity which is the trademark of a Jew, remains unblemished, the Torah instructs us to eat only Kosher animals.