Keep Reading

Usually happens in movies. A piece of writing appears, and instead of just pointing the camera at it and making the audience read it, which would be boring, a character is forced to read it out loud. This despite the fact that it's rather unnatural for him to do so in the given situation, when in real life he would just read it quietly. For example, there might be only two characters present, one of which has already read the text.

To help him along, another character (in the above example, the one who knows the text already) would command him "Read it!" The reader, aware of how unnatural it is to just read a text out loud, will often even pause in the middle, and must then be prodded to "Go on!" by the first character.

This trope refers only to those situations where a text is read out loud (not in a voice-over), and the reading-out-loud is clearly forced in for the benefit of the audience. (Not if, say, a character was gonna read a text to a group anyway.)

Examples of Keep Reading include:

Film

In the film version of Harry Potter and the Prisoner of Azkaban, when the Marauder's Map insults Snape, he angrily hands it to Harry and orders him to read it. As is typical, Harry hesitates halfway through, because he's nervous about reading a text that insults Snape, but Snape calmly tells him: "Go on."

Live Action TV

In an early episode of Lost, Sawyer shows Kate a letter supposedly written to him by a little boy. When she stops reading, he says "Oh don't stop now!" implying the most dramatic part of the letter is yet to come. It partially happens again in a season three episode, when Sawyer hands the letter to Anthony Cooper, the person it's intended for, ordering him to read it. But this time the letter isn't read in its entirety, so presumably, the audience is expected to know what it contains. (Also, in the second setting, the reading-out-loud is a bit more natural.)
Veronica Mars: In the second episode, Veronica discovers that the student who hired her double crossed her by making her look for his deceased dad, who he knew was dead. She confronts him with a copy of his school records which she demands he read aloud.

Musicals

Played with in Nunsense: During the skit where three nuns try and sell their cookbook, they read it aloud for the audience's benefit as there is no fourth wall, and they know that the audience is there. However, one of the nuns, Sister Amnesia, is a little on the slow side and has to be prodded into reading her recipe out loud.