These constant are used with several events, and allow you choose whether action that is to be taken by the user will be allowed or not. For instance, when user provides username/password combination, Connected event will be fired with following parameters:

Private Sub Pop3_Connected(ByVal User As wodPop3SERVERLibCtl.IPop3User, ByVal Username As String, ByVal Password As String, Action As wodPop3SERVERLibCtl.Pop3Actions)
     If Username = "test" And Password = "test" Then
        Action = Allow ' allow user to login
    Else
        Action = Deny
    End If
    '.......
End Sub

In above sample, only user 'test' with password 'test' is allowed to login - all others are rejected from server.