What does Mark 2:10 mean?

All of the things Jesus has done—heal people, expel demons, reveal hidden thoughts—must have been accomplished through the same power and the same authority: that of God. Isaiah 35:6 says that the Messiah will heal the lame. Psalm 139:1–2 says that God knows men's thoughts. As with the prophets of the Old Testament, these miracles should prove to the scribes that Jesus is working with God's authority because He has been granted God's authority. And if He has God's authority to heal, He has God's authority to speak for God. So when Jesus declares that the sins of the paralyzed man are forgiven, He is speaking for God.

The term "Son of Man" is from Daniel 7:13–14. In the end times, one "like the son of man" will be presented to the Ancient of Days and given everlasting dominion over the peoples and nations. Jesus expands this to say the Son of Man has authority to forgive sins. The scribes don't understand from Jesus' teaching and miracles, so Jesus spells it out for them: He is the Messiah.

"Son of Man" also identifies Jesus as human. He is fully God and fully man. Because of His humanity, He can be the sacrifice for our sins. Because of His deity, His character has the purity needed to make that sacrifice worthy. Jesus is called the "Son of Man" nearly ninety times in the New Testament, mostly by Himself, including in the prophecies that the Son of Man must suffer many things and be rejected (Mark 8:31), and will rise from the dead (Mark 9:9). Mark uses the title fourteen times in his Gospel.

In the next verses, Jesus will use this combination of prophetic attributes to prove that He does, in fact, have the ability to forgive sins. When the lame man starts to walk, it's a physical sign of Jesus' power.