If you dreamed of walking up the stairs, then such dream shows that you are going on the right direction and getting to the point where you supposed to be. The stairs also opens the view which you show for the others of what you have achieved and confronted. If the one was walking down the stairs, then such dream could mean that you are not making any progress anymore, instead you let not only other down, but yourself either. Make sure you do not give up and climb those stairs as the winner. The dream could also indicate your thoughts and feelings that are coming from the past, therefore you are going down the stairs and confront things that are no longer important in the present.
Read more about dreaming of Stairs in other dream meanings interpretations.