Purpose of dialogue

To develop the plot of the story. For instance, the antagonist might say something that angers the protagonist. This anger causes the protagonist to take some sort of action, moving the plot closer to its conclusion.
To reveal conflict between characters. For instance, the dialogue between two characters might be hostile or full of invective, which reveals the conflict between two opposing forces.
To develop the personality of the character. Both the tone and content of the dialogue tell the reader about the nature of the character. For instance, if the character speaks well and uses eloquent words, the reader draws the conclusion that the character is educated and intelligent.
To reveal background information about a character. The writer can use dialogue to reveal something that happened in the past