Sin requires a payment, and throughout the Old Testament God established that the sacrifice had to be without blemish. The Passover lamb and the sacrifices under the Mosaic law all pointed forward to Jesus Christ, the perfect sacrifice who would one day come into the world. Unlike every person born into sin, Jesus was completely sinless, and because of that He alone could pay the penalty for the sins of mankind.
When Jesus went to the cross, He willingly gave His life for us. The Old Testament sacrifices could only picture what Christ would accomplish, but Jesus, the Lamb of God, came to take away the sin of the world. Though He was examined and found without fault, He was still condemned to die so that sinful man could receive forgiveness and eternal life through Him.