Mikhail Bakhtin wrote extensively about this aspect of Crime and Punishment. "Dialogic" is the opposite of "monologic." We all know that a dialogue is two or more people talking, while a monologue is just one person talking. You might have heard the phrase "internal monologue," used to refer to what happens in a book when we are inside a character's head, reading that characters inner thoughts. In the case of Crime and Punishment, we more often find "inner dialogues" than "inner monologues."
What goes in Raskolnikov's head after he reads the letter from his mother is a good example. He's literally talking to himself while he walks, but he's also talking to Pulcheria, Dounia, and Sonia. Of course, none of them are there. Raskolnikov hasn't even met Sonia yet – he's only heard about her from Marmeladov.
The narrator, on the other hand, seems to be speaking directly to the readers, sometimes giving us little tidbits of information that doesn't seem to be coming from any of the characters. This mostly happens when politics and philosophy are topics of conversation. Here's an example from the section that is split between Andrey Semyonovitch Lebeziatnikov and Pyotr Petrovitch Luzhin:
He, like everyone, had heard that there were, especially in Petersburg, progressives of some sort, nihilists and so on, and, like many people, he exaggerated and distorted the significance of those words to an absurd degree. (5.1.6)
It can't be Andrey Semyonovitch's perspective, and it can't be Luzhin's. It has to be the narrator's (and Dostoevsky called the narrator "the author").
Bakhtin says that Dostoevsky was obsessed with the power of "ideas," which we hear so much about in the novel, but that ideas were nothing until they were put into dialogue with other ideas. One could only "test" or bring an idea by exposing it to many different kinds of people.
Stylistically, this can be a test to our patience and reading skills. We're sure you noticed those multi-page paragraphs full of different voices and perspectives. This confusing, bulky style in some ways mirrors the confusion of the times, which Dostoevsky was trying to capture.
Dostoevsky's dialogic style in Crime and Punishment is also loaded with repetitions – of stories (like the stories of Svidrigaïlov's servant and the young he drove to suicide), images (crosses, blood), and ideas. So, if you miss something the first time, it will more than likely show up again, half a dozen times.