In this passage Jesus demonstrated yet another realm of his authority. He is the one who has the authority to forgive sins.
The power and authority of Jesus attracted large crowds and spectators in Matthew 8. Many expressed a desire to follow Jesus. Yet for many, what they were attracted to was not actually Jesus, but his power. Hence, when Jesus describes the cost of descipleship, many turn away.
Immediately after the Sermon on the Mount, Jesus validates his authority by healing many in Capernaum and the surrounding region. Jesus' power and authority transcend all disease, races and geography. He is Lord over all. His miracles are acts of loving kindness to those whom he heals and powerful confirmation that the Kingdom of God is present in his ministry.
Jesus concludes the Sermon on the Mount with 4 warnings, Jesus forces each of us to make a decision about Him. He will not let us remain neutral. Either we choose to listen and obey Jesus or we reject Him and go our own way. The former leads to eternal life, the latter leads to destruction.