Okay, nice and simple. Human beings do evil stuff. God's character has two major sides - justice and mercy. Justice requires that God punish evil, the punishment being a kind of eternal death, or what we call hell, which we don't know that much about but we do know is pretty unpleasant (flames and darkness and agony and stuff) and goes on forever. Justice does allow a substitute, as in, someone else to take the punishment. God sends Jesus, his son, who is also in some way God himself (see The Trinity) who must a) himself live a perfect life, and never do anything evil, and b) take everyone's punishment himself. He successfully achieved both these things, and did not remain in hell because he didn't really deserve to. What he suffered was enough, however, to allow every human being (past, present and future) to be granted an unconditional pardon.
The catch, if you can call it that, is that the pardon has to be accepted, for which we need to believe that Jesus' substitutory punishment did actually take place, and that he was actually both God and human. (I understand this as him being human in every way, only having the same personality as God - not the same knowledge or intelligence, just the same character.) Accepting the pardon also involves a promise on our part, to try to stop doing evil stuff - this invariably means accepting God's way of living life as the way to go, rather than our own. Note that success is not required - the pardon can be renewed again and again - all that's required is to care enough to try.
And that's it!