C.S. Lewis gives a good answer to essentially this question in God In The Dock: Essays on Theology and Ethics.
I can’t say for certain which bits came into Christianity from earlier religions. An enormous amount did. I should find it hard to believe Christianity if that were not so. I couldn’t believe that nine hundred and ninety-nine religions were completely false and the remaining one true. In reality, Christianity is primarily the fulfillment of the Jewish religion, but also the fulfillment of what was vaguely hinted in all the religions at their best. What was vaguely seen in them all comes into focus in Christianity – just as God Himself comes into focus by becoming a Man.
One observation often made is that the Golden Rule, which is absolutely central to Christian ethics (see, for example, Mark 12:28-31, Matthew 7:12, Romans 13:9), is found in many earlier sources as well. Indeed, the idea is found in Buddhism, in Confucius, in the Greek philosophers, and in Judaism as well (Leviticus 19:18). Christ references it as being an existing commandment. If this is surprising to anyone, it is a result of a misunderstanding about Christ’s mission. Christianity does not introduce a novel system of ethics. Rather, Christ calls people back to the straightforward morality that each of us already knows. Jesus doesn’t present the moral law as new information; for example, at the end of the parable of the Good Samaritan, He asks the listener who the “neighbor” is. Jesus knows that the listener will see it on his own. Saint Paul makes a similar point in writing that the law is written on our hearts.
This is not to say that Christianity is simply a restatement of earlier traditions. While the ethical core is the same, Jesus expresses it very broadly, focusing on the positive manifestations of loving one’s neighbor rather than the negative form (sometimes called the Silver Rule) of simply “do no harm”. Neglecting to show love becomes as serious a sin as doing harm. Christ simultaneously strips away the fluff with which organized religion often surrounds the Golden Rule, yet also takes the moral law to its uncomfortable logical conclusions, illustrating perfection and total commitment. We know that what He teaches is correct, but no one can live up to that standard.
So if Christ’s mission wasn’t to introduce a new system of ethics, what was it? Succinctly stated, it was to save us from our sins. God is perfectly just, so our sins must have consequences. God is holy, so our sin separates us from Him. Christ’s mission was to solve this problem for us, since we are not capable of solving it ourselves. How does He do this? Admittedly, the process of it is somewhat mysterious, as are the reasons why it had to happen the way it did. In another post, I try to shed some more light on the topic and speculate on why sin couldn’t simply have been pardoned without the sacrifice of Christ on the cross.
Another charge often made is that some elements of the Christian narrative have parallels with myths of other religions. C.S. Lewis deals with this at length in an essay, Myth Become Fact, which in turn has been ably explored here by Bruce Young.