Jewish people believe that God commands kosher laws. Moses taught these rules to God’s followers and wrote the basics of the laws in the Torah. By eating kosher food, some Jewish people believe it helps them feel connected to God.
The basic laws of kosher (or kashrut) are of Biblical origin (Vayikra 11 and Devarim 17). For thousands of years, rabbinic scholars have interpreted these laws and applied them to contemporary situations. In addition, rabbinic bodies enacted protective legislation to safeguard the integrity of kosher laws.
Many modern Jews think that the laws of kashrut are simply primitive health regulations that have become obsolete with modern methods of food preparation. There is no question that some of the dietary laws have beneficial health effects. For example, the laws regarding kosher slaughter are so sanitary that kosher butchers and slaughterhouses are often exempted from USDA regulations.
However, health is not the main reason for Jewish dietary laws and in fact many of the laws of kashrut have no known connection with health. To the best of our modern scientific knowledge, there is no reason why camel or rabbit meat (both treif) is any less healthy than cow or goat meat.
In addition, some of the health benefits derived from kashrut were not made obsolete by the refrigerator. For example, there is some evidence that eating meat and dairy together interferes with digestion, and no modern food preparation technique reproduces the health benefit of the kosher law of eating them separately.
The short answer to why Jews observe these laws is because the Torah says so. The Torah does not specify a reason for these laws but for an observant Jew there is no need for a reason - Jews show their belief and obedience to God by following the laws even though they do not know the specific reason.
In the book To Be a Jew, Rabbi Hayim Halevy Donin suggests that kashrut laws are designed as a call to holiness. The ability to distinguish between right and wrong, good and evil, pure and defiled, the sacred and the profane, is very important in Judaism.
Imposing rules on what you can and cannot eat ingrains that kind of self control. In addition, it elevates the simple act of eating into a religious ritual. The Jewish dinner table is often compared to the Temple altar in rabbinic literature.