See this passage explained in the notes at Matthew 20:29-34.
Blind Bartimeus - Matthew says there were two. Mark mentions but one, though he does not deny that there was another. He mentions this man because he was well known - Bartimeus, the “blind man.”
Casting away his garment - That is, his outer garment - the one that was thrown loosely over him. See the notes at Matthew 5:40. He threw it off, full of joy at the prospect of being healed, and that he might run without impediment to Jesus. This may be used to illustrate - though it had no such original reference - the manner in which a sinner should come to Jesus. He should throw away the garments of his own righteousness - he should rise speedily - should run with joy - should have full faith in the power of Jesus, and cast himself entirely upon his mercy.