The Redirect URI for OAuth is used as the way for the OAuth provider (in this case, Constant Contact) to send secure responses to the OAuth consumer (in this case, your application). It is set as part of the application key configuration so that Constant Contact knows who to send the responses to and is used often as a way to avoid impersonation and some forms of man in the middle attacks.
This is important as OAuth flows require that the end user of the integration must go through the OAuth provider (Constant Contact) login page in order to identify themselves. Since this page is hosted by a 3rd party and not your application, the success/failure criteria must be communicated back to you through a redirect. This is where the redirect URI comes into play. When the login is processed, we redirect to your URI to share the success or failure information of the flow so you can process the access_token and store it for future use securely.
Dave Berard Senior Product Manager, Constant Contact