There are a number of different ways that Christians answer this question.
One way I've heard is, granted, not fair to the Jews, but it is compatible with what gets said in the NT.
The 613 mitzvot (commandments) in the OT are detailed prescriptions for how to handle detailed legal issues. For example, what happens if your neighbor's cow eats your grapes. Despite the large number of rules, however, no specific set of laws can cover every possible moral issue in the world. It also leaves the follower open to the criticism of legalism -- that one merely has to follow the letter of the law and not its spirit, so that there will always be loopholes and ways to do what you want that don't seem very ethical, because none of the 613 addresses exactly the situation you're in.
(The Jews, of course, deny these criticisms -- they'll point out for example that the commandment not to work on the Sabbath is not absolute -- if someone is sick then the ambulance driver ought to go to work. People's well-being may overrule the mitzvot. So the accusation of legalism is, to them, unfair.)
What happens in the NT is that Jesus says he has come to "fulfill" these mitzvot. Many interpret this to mean that instead of a detailed adherence to the letter of the laws, we are to obey the main spirit behind them. This is identified in the NT as the "Great Commandment":
Quote:"'You shall love the Lord your God with all your heart, and with all your soul, and with all your mind.' This is the greatest and first commandment. Love God above all else. And the second is like it: 'You shall love your neighbor as yourself.' On these two commandments hang all the law and the prophets."
— Matthew 22:35-40
Though the sense of all the OT commandments are boiled down to two, in fact these two are harder to keep. If the commandments are detailed and specific you know if you've kept them or not. But if the commandments are so general -- "love everybody" -- one is left in doubt as to whether one has done enough.
I've heard the difference compared to the instructions you give a little child compared to what you say to an older person. To a kindergarten student, you give specifics: "don't get in anybody's car; don't speak to strangers; don't go into any stores on the way home; don't take candy from strangers." These are detailed rules because a small child won't be able to make good judgments for himself. If we just say "be safe" to such a small child, that's not enough, because they don't know how to be safe. Older children, however, are more capable of making judgments about what is and isn't safe. For them, the letter of the law is less important than the general goal. So the OT laws are what you'd tell to beginners, while the NT is for those who make their own judgments.
Again, it's rude to the Jews to describe them as child-like. But this is a common Christian interpretation.