There's no better way to talk about tone than to look at an example from the text. So, let's get right to it! Here's a lovely chunk of dialogue and commentary that comes from Chapter 39, "Wickfield and Heep." David meets up with Mr. Micawber again now that Mr. Micawber has become Uriah Heep's law clerk and works regularly in the Wickfield house. Things are a bit strained between David and Mr. Micawber because Mr. Micawber refuses to talk smack about his new employer, Uriah Heep – who David clearly hates. So, they're searching for new, less touchy topics of conversation. Mr. Micawber turns the discussion to Agnes Wickfield, whom he likes very much. Mr. Micawber adds:
"If you had not assured us, my dear Copperfield, on the occasion of that agreeable afternoon we had the happiness of passing with you, that D. was your favourite letter," said Mr. Micawber, "I should unquestionably have supposed that A. had been so."
We have all some experience of a feeling, that comes over us occasionally, of what we are saying and doing having been said and done before, in a remote time – of our having been surrounded, dim ages ago, by the same faces, objects, and circumstances – of our knowing perfectly what will be said next, as if we suddenly remembered it! I never had this mysterious impression more strongly in my life than before he uttered those words. (39.27-28)
Sorry, this is a mouthful. But we think it's a useful illustration of the three main aspects of the tone of David Copperfield. First, it's funny. Okay, this is not the funniest section of the book (personally, we really like Chapter 24, "My First Dissipation," the chapter about David's drunken revels with Steerforth.) But it still has signs of that wry sense of humor that spreads through the whole novel.
Mr. Micawber won't come out and say, you should have a crush on Agnes! That girl's awesome! Instead, Mr. Micawber refers teasingly to a moment in Chapter 27, when Traddles and the Micawbers come to David's apartment in London and mock him for his latest crush, this time, on a girl whose name starts with the letter D (Dora!). This modest humor is really characteristic of Dickens's writing; we can see signs of it throughout the novel, from the "Brooks of Sheffield" episode in Chapter 2, to Mr. Micawber's hilarious outburst against HEEP in Chapter 52. Dickens uses humor to lighten up really serious subjects, in this case, David's huge mistake in preferring Dora to Agnes.
Immediately after Mr. Micawber's mild joke comes some intense commentary. David stops the narrative to tell the reader about the experience of déjà vu, when we "[know] perfectly what will be said next, as if we suddenly remembered it!" By stopping the dialogue here to throw in this bit of extended commentary, narrator-David is drawing our attention to the importance of what Mr. Micawber has just said. He is foreshadowing that Mr. Micawber is right: "A" is better for David than "D."
As a character, David may not understand why Mr. Micawber's words have so much impact on him, but as a narrator, David is perfectly aware of why this statement is so important. By inventing a first-person narrative voice who is looking back on the (fictional) events of his own life, Dickens is giving us a plot-level reason for why there is so much foreshadowing in this book.
And if there's one thing foreshadowing achieves, it ratchets up the drama. We know that something pretty dire involving "A" and "D" must be heading David's way, because the narrator bothers to stop and tells us about the character's profound sense of discomfort: déjà vu that he experiences "never [...] more strongly in [his] life than before he uttered those words" (39.28).
Yet, at the same time, there's no way that, at the time, David can really know why these words strike him as so threatening. Only the narrator knows. So Dickens is bending the rules of probability to achieve a dramatic effect. It's not at all realistic that David would feel that he has heard Mr. Micawber's teasing words about "A" and "D" before. But it does give us a strong emotional thrill that something is about to happen. So, that's why we say that Dickens's tone is often melodramatic: he bends the rules of realism and cause and effect to give his stories more emotional impact.