Another way I have found effective to explain to children Christ's substitutionary atonement:
"While Jesus was on the cross, God took all of your sins off of you, put them on the Lord Jesus and punished Him as if He was the one who did them instead of you. He said, "It is finished." Since Jesus did everything that needed to be done to pay for your sins, all that is left is for you to believe Him and receive Jesus as your own Savior." (John 1:12)
Of course, never forget to also tell them that Jesus didn't stay dead, but came back to life on the third day.