Yes, that is what Christians believe.
Why do they believe it though? Its a tenant of their faith that mankind is guilty in the eyes of God. Their God sees things as kind of binary - good - heaven, bad - hell. The standard is impossible for humans to meet, even the littlest indulgence of a bad thought = hell. But they teach God is actually a three part being, one part of which is Jesus, who accepted guilt for all of mankind's sins. He died and this burden of guilt for all sins died with him, but rose from the dead having conquered sin (physics doesn't explain this, you just have to believe it or not). Here is the catch - those who believe this story and feel remorse for the bad things they have done to the point where they will try to behave righteously can accept forgiveness and their guilt is considered to be absolved by Jesus' death with the burden of all man's sins and those who do not have to be punished for the sins' themselves.
How do the metaphysics of this all work? I read fantasy novels for fun, but this is something the human mind probably just can't understand other than the general concepts.
Why do people have to accept Jesus' resurrection to be absolved of sin? The resurrection is part of overcoming the sin - basically Jesus is so good that it outweighs all the bad everyone has ever done in a way that the deeds of the best saint on earth can't even do. And because otherwise there would be no need for adherents of the Christian faith to proselytize and the religion would die out quickly.