Every component of narrative fiction must be there to serve a purpose. Nothing is included just for the heck of it. The setting, the description, the exposition and even the most minor character should be necessary to further the plot. And this rule of necessity also applies to dialogue. 

The difference between a real-world and a fictional conversation is that the latter is part of a bigger narrative and exists solely to further its narration. And your dialogue must achieve one or more of these purposes: aid characterization, supplement exposition and advance narration.  

Dialogue Tells us More about a Character.

Although dialogue doesn't do most of the heavy lifting in characterization, it is not out of place to use them to show certain traits and mannerisms of a character. It has been used to exhibit a distinct set of diction that explains a character's background and disposition. Famous authors like George R. R. Martin have used dialogue to show some of their characters having a particular dialect or catchphrases. 

Beyond accent and pattern of speech, you can also use dialogue to perfectly portray the desires, fears, aspirations and intentions of characters. Readers can get a character's point of view and understand the reason behind his actions from what he says and how he says them. A character's speech can indirectly express much about his inner thoughts.

What a character says can also tell readers where they belong in society, how they feel about various topics and their opinion about other people. It can display if a character is rude or polite, jovial or uptight, sophisticated or simple, experienced or naïve. 

Fictional characters converse the same way and for the same reasons that real people do; their conversations also contain real-world elements of misdirection, confusion, and shyness. Dialogue can hide a character’s intent as well as show it. Often, the meaning of a conversation is more present in what is left unsaid than what is said. And what a speech hides also tells us more about the speaker.

Dialogue Tells us the Story.

Many stories are told mainly through the use of dialogue. A legal thriller could include a discourse of witnesses during examination-in-chief that reveals a large part of the narrative. Or it could use cross-examination dialogue to deliver a bombshell revelation. Many writers of crime narratives and detective stories use dialogue to narrate most, if not all, of the stories. 

Most mysteries consist of two stories told at the same time. First is the chronological account of the investigation. Then, there is the series of events leading up to the crime, narrated in bits and pieces from the dialogue of witnesses and suspects. Examples of this structure abound in most of Sherlock Holmes stories.

Even the subtleties in dialogue also help advance the plot of a story. Sometimes, the subtext in a conversation tells the complete outcome of a scene. A classic example of this is the dialogue about mushrooms between Sergei Ivanovich and Varenka in Anna Karenina. Their mushroom discussion turned out to actually be about the end of their engagement. 

Dialogue Gives us More Information.

Characters can, through dialogue, explain a backstory or deliver some essential details about the narrative to the readers. This is known as expository dialogue. Here, historical facts and explanations of some events in the story are contained in conversations between characters.

Some narrative fiction includes a designated minor character, whose role is to appear from time to time to give a backstory or an explanation. This is the role of Dr Mortimer in Hound of the Baskervilles. But this approach is often less compelling than the rest of the story. And sometimes, a better method could be to provide the information directly in prose format. But if it must come from the words of a character, make him a first-person narrator or deliver it with indirect dialogue.