This phrase is best understood within the context of the paragraph in which it appears; Montresor is talking about the need not only for vengeance against Fortunato, but vengeance that is conducted in a particular way.
I must not only punish, but punish with impunity. A wrong is unredressed when retribution overtakes its redresser. It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong.
"I must not only punish, but punish with impunity" - impunity basically means exemption from punishment or vulnerability. Montresor needs to punish Fortunato in a way that will not cause Montresor to be punished, himself. He's basically saying that he needs to think of a way to take his revenge that will protect him from suspicion and ensure that he gets away with it.
"A wrong is unredressed when retribution overtakes its redresser." The word "redress" means to fix or set right. Thus this sentence might translate to, "A problem is not set right if revenge overtakes the person trying to fix it." Montresor is saying that he needs to keep his wits about him and avoid being overcome by emotion, or by the manner in which he conducts his revenge - otherwise, being punished for what he's going to do to Fortunato will make it look as though the justice of his actions is not complete.
"It is equally unredressed when the avenger fails to make himself felt as such to him who has done the wrong." The person who committed the crime needs to know that his actions have brought revenge upon him, and that revenge is what is taking place, rather than some sort of accident or unrelated offense. Montresor needs Fortunato to know that he is being punished, otherwise his crimes are not fully addressed because Fortunato will not know why this is happening.