I have listed below three important quotations from the film, and for each quotation I have tried to explain why the quotation qualifies as important. The first quotation is taken from about nine minutes into the film.
We’ve become a race of Peeping Toms. What people ought to do is get outside their house and look in for a change.
This is an important quotation because it encapsulates one of the main moral messages of the film, namely that we should focus more on our own lives, and on our own inadequacies, and less on the lives and perceived inadequacies of others. This is what Stella means when she tells Jeff that we should look into our houses more often, rather than looking out of them and into the houses of others. Jeff of course ignores Stella's advice, and becomes more and more engrossed in what is happening in the apartment opposite his own. This obsession eventually costs him dearly. Indeed, he breaks his leg again and is confined to his wheelchair for a longer period of time.
Another important theme in the film is the theme of love and commitment. Jeff is himself afraid of commitment, as exemplified by his reluctance to commit to Lisa. In this second quotation, below, Jeff is talking to Stella. The quotation is taken from about forty minutes into the film.
Sometimes it is worse to stay than it is to run.
Ostensibly, Jeff is here talking about his neighbor, Mr. Thorwald. Jeff believes that Mr. Thorwald is about to leave his wife, probably because they argue so often. Jeff is implying that sometimes it is better to leave a marriage than to stay in it, especially if to stay in it means to constantly argue. Implicitly, Jeff is also here alluding to his own inability, or unwillingness to commit to Lisa. Jeff prefers to “run,” because he thinks the alternative is to be, metaphorically, tied down. The irony at this point in the story, of course, is that Jeff, confined to a wheelchair, is unable to run. Nonetheless, he still avoids committing himself to Lisa, and chooses instead to commit himself to a voyeuristic obsession with his neighbour, Mr. Thorwald.
In the third quotation, below, Detective Doyle warns Jeff about his voyeurism. This third quotation is from about one hour and fifteen minutes into the film.
That’s a secret, private world you’re looking into out there. People do a lot of things in private they couldn’t possibly explain in public.
In this third quotation, Detective Doyle reiterates the message from the first quotation. He points out to Jeff that everybody, including Jeff himself, is guilty of “things” in private that could not be explained in public. Indeed, Jeff’s behaviour in his own apartment, seen by somebody else looking in, might seem very suspicious, and might be difficult to explain.