The meaning of this scene was mainly enhanced by the improvisation of Robert De Niro.
The scene where Travis Bickle is talking to himself in the mirror was
completely ad-libbed by Robert De Niro. The screenplay details just
said, "Travis looks in the mirror." Martin Scorsese claims that he got
the inspiration for the scene from Marlon Brando mouthing words in
front of a mirror in Reflections in a Golden Eye (1967).
IMDB: http://www.imdb.com/title/tt0075314/trivia
Another reference is found here which links this dialogue to Bruce Springsteen
Robert De Niro improvised that whole paranoid monologue, including
what would become the movie’s most famous line. (The film's
screenwriter, Paul Schrader, later said, “It’s the best thing in the
movie, and I didn’t write it.”) De Niro got the line from Bruce
Springsteen, whom he’d seen perform in Greenwich Village just days
earlier, at one in a series of concerts leading up to the release of
Born to Run. When the audience called out his name, The Boss did a bit
where he feigned humility and said, “You talkin’ to me?” Apparently it
stuck in De Niro’s mind.
http://mentalfloss.com/article/67148/13-grimy-facts-about-taxi-driver
Now, to ans your question, more specifically,the cinematography and the props rather the Mise-en-scène, were not the major reasons why this scene became iconic. We are talking about 1976, where in motion pictures, improvisations this long and detailed were quite rare.
Martin Scorsese here himself explains how the shot went.I would rather request you to watch it. Its interesting! It's at 3:57