They bring - That is, his friends brought, or the people brought.
One that was deaf, and had an impediment in his speech - Not entirely mute, but who spoke indistinctly or with difficulty. His deafness might not have been of long standing, and his speech, therefore, not entirely ruined.
To put his hand upon him - That is, to cure him. Blessings were commonly imparted by laying on the hands.