There are typical ideas of "men": usually older movie stars when they were younger, usually working class, usually troubled, and almost always hot-headed and masculine. Marlon Brando is a very classic example of this, perfectly executed in On the Waterfront.
Unlike his character in A Streetcar Named Desire, where he is incredibly manly but also incredibly antagonisty, in On the Waterfront he is a guy to root for. You don't know much about his life--where his parents are, how old he is, how he grew up, even what town he currently lives in--but you can infer what kind of life he led and leads. He works a dead end, dangerous job. He also works as a lackey for the union at said job. He once aided in killing a man, without realizing it.
And yet, women, both fictional and real, are drawn to him. Maybe it is because he is a sensitive and tortured soul, forced to grow up hard and tough, because that is the life he was born into. Characters like this are always intriguing, because they have become cliche. But when Brando plays it, it isn't cliche. It is true and you can tell that Brando is killing himself in this role. That is what makes this movie so memorable.
It doesn't hurt that Elia Kazan directed it and the plot is killer and the supporting cast is fantastic.