The Shady Character is a representative of smugglers who operate out of the City of Amaranthine.
When the Warden-Commander first enters the city, the Shady Character will announce that he has a proposal, and invites the Warden to speak to him if interested. He will offer a share of the profits in exchange for the Warden-Commander's help in preventing the Amaranthine City Guard from interfering.
Accepting his offer results in starting a profitable, although not morally correct quest Smuggler's Run. Should the Commander refuse his offer they can let him leave or kill him. Regardless of what happens if the Commander later sides with the City Guard in shutting down the smugglers during Law and Order he will appear by the hidden entrance to the Smuggler's hideout beneath the city to let the suspicious character in through the hatch and will attack the Grey Wardens.