When Jesus' body died on the cross, He didn't cease to exist any more than we do when our bodies die. His soul or spirit kept on living just as ours will when we die. Almost His final words from the cross were these: "Father, into your hands I commit my spirit" (Luke 23:46).
But Jesus' spirit was different from ours and one of the ways it was different was its absolute holiness and purity. We are sinners, stained by our disobedience and rebellion against God. But Jesus was without sin; in fact, He bore in His spirit the very nature of God Himself. As the Bible says, "He is the image of the invisible God. ... For God was pleased to have all his fullness dwell in him" (Colossians 1:15, 19).
Jesus' spirit, however, was different from ours in another way: On the cross, all the sins of the human race were poured out upon Him. He was without sin but on the cross, all our sins were placed on Him, and He took the judgment and Hell we deserve so we could be forgiven and saved. Our sins were transferred to Him and His righteousness was transferred to us.
We will never fully understand the wonder and mystery of Christ's nature and His sacrifice for us not until we enter heaven. But don't let that keep you from Christ! God loves you, and the proof is that His Son was willing to give His life for your salvation. By faith open your heart to Him today.