What do the Puritan magistrates hope to accomplish with this punishment? (The punishment for Hester Prynne of Adultery)

In
addition to the other excellent answers, I
would add that one must consider the beliefs of the
Puritans.  They were
constantly looking for verification that someone was or was not a
"chosen"
one of God, destined for the kingdom of Heaven.  By brandingin this way, it

was one less to worry about (there were only so many spots, you see) but also
benevolently
consorting with Hester in any way might also indicate to others
that the consorter was one of
the lost.  I know it's confusing, but that's
the way it worked.  "Who's in, who's out"
was constantly on the Purtian radar
(so to speak).