The Jews recognize three categories of Old Testament laws: mishpatim, eduyot, and chukim.
*]Mishpatim are laws with a clear moral and societal benefit, like “Thou Shalt Not Kill.” Many of these laws can be deduced from natural law – that is, even without the Ten Commandments, we could determine that murder is wrong from reason and conscience.
*]Eduyot are those laws governing particularly religious things, like the Sabbath and holy days. These are **not **things which could be known from nature, but they **are **things with a clear moral benefit.
*]Chukim is the third category. These are laws which appear completely arbitrary, like the prohibition against eating shellfish or wearing mixed-linen clothing. They don’t have an intrinsic moral benefit, in the laws on murder or the Sabbath do.
Your question is about this third category. The moral benefit of this category of law was made very clear by the New Testament. Like Petergee said, these are laws which foreshadowed Christ, and exposed the need for Him. The Law in general does this in a few ways:
*]It calls the people to holiness, in both senses of the word. “Holy” means “set apart.” So the Jews weren’t allowed to mingle, and were always required to do things, wear things, and eat or not eat things, which singled them out as Jews, and not as pagans. They were also called to holiness in the other sense, of giving yourself over to God. The two types of holiness go hand-in-hand: Think about the Roman collar that Catholic priests wear - it shows them at once to be priests, and is directly tied to their calling to be moral examples to those around them.
*]It reminded the people of the gravity of their sin. This also deterred sin – if the price of sinning was that you lost a very valuable animal, you’re less likely to do it.
*]It showed the Jews the need for a Messiah. Even with this awareness of their sin, and even with the high earthly price of sin, people kept right on sinning, because of original sin and our fallen nature. As the Old Testament unfolds, you see the authors’ increasing awareness that they **can’t **be righteous on their own.
*]The Law had an obsession with purity and spotlessness. God is pure Goodness, and cannot be in the presence of sin. The Law reflects this - anything symbolizes impurity (spots on an animal, patches on clothing, etc.) was rejected. Shellfish, for example, aren’t clearly fish and aren’t clearly reptiles, so the Jews were forbidden to eat them. From either perspective, they’re imperfect, and fall into a gray area.
*]Related to #4, the Law is premised on this idea of choosing one or the other, and not trying to have it both ways by being a little Jewish and a little pagan. Deuteronomy 30:19 says it clearly: “This day I call heaven and earth as witnesses against you that I have set before you life and death, blessings and curses. Now choose life, so that you and your children may live!” In the end, there’s Heaven and Hell, no middle option. The Law hammers this life or death notion in at every possible turn.
*]Finally, there are a lot of specific Christological prophesies, like the curse upon He who hangs on a tree, which Paul explains as foreshadowing Christ’s suffering on the Cross.