The Shrouded Man was summoned by Richard Wilkins in order to perform a ritual to remove Angel's soul. Faith Lehane, the rogue Slayer at Wilkins' service, helped the shaman perform the ritual by spilling unconsecrated blood on Angel's chest.
However, it is revealed later that the ceremony was nothing more than a "light show". The Shrouded Man was in league with Rupert Giles, having warned him of Wilkins' plans, joining the plot to mislead the Mayor and extract information from Faith, of whom Buffy Summers and Giles had become suspicious. With his aid, he considered the debt he owed Giles, having introduced him to his wife, was repaid in full. Afterward, he disappeared, but not before warning Giles not to summon him ever again.
Powers and abilities
"Thank you for coming to me. And for that rather effective light show you put on."
The Shrouded Man had the ability to teleport from and to areas with little or no light, possessed telekinetic powers, which he used to levitate Angel during the false ritual, and was also capable of creating "light shows".
As Richard Wilkins summoned him for that purpose, it is likely that the Shrouded Man was actually capable of removing souls from individuals, though he never actually demonstrated it.
Behind the Scenes
He was portrayed by Gary Bullock.
The Shrouded Man looked very similar to the members of The Tribunal. It is unknown whether they belong to the same species or if the Shrouded man is actually one of the Judges.