Narrative exposition is the insertion of background information within a story or narrative. This information can be about the setting, the characters' backstories, prior plot events, historical context, etc. In literature, exposition appears in the form of expository writing embedded within the narrative. Exposition is one of four rhetorical modes (also known as modes of discourse), along with the description, argumentation, and narration, as elucidated by Alexander Bain and John Genung.
Nothing will slow down plot faster than an information dump (or "infodump"). This is where the author merely tells the reader something he thinks the reader needs to know before moving on with the plot. It's bad enough when this is done in the narrative, but dreadful when done in dialogue. In certain contexts this might be perfectly fine: Sometimes telling is a short cut, and if it is indeed short, it can work. But exposition in fiction works best if it is embedded in the action, only about ten percent of the information is given, and ninety percent remains hidden and mysterious below the surface.
Indirect exposition, sometimes called incluing, is a technique of worldbuilding in which the reader is gradually exposed to background information about the world in which a story is set. The idea is to clue the readers into the world the author is building without them being aware of it. This can be done in a number of ways: through dialogues, flashbacks, characters' thoughts, background details, in-universe media, or the narrator telling a backstory. Instead of saying "I am a woman", a first-person narrator can say "I kept the papers inside my purse." The reader (in most English-speaking cultures) now knows the character is probably female.
Indirect exposition has always occurred in storytelling incidentally but is first clearly identified, in the modern literary world, in the writing of Rudyard Kipling. In his stories set in India like The Jungle Book, Kipling was faced with the problem of Western readers not knowing the culture and environment of that land, so he gradually developed the technique of explaining through example. But this was relatively subtle, compared to Kiplings' science fiction stories, where he used the technique much more obviously and necessarily, to explain an entirely fantastic world unknown to any reader, in his Aerial Board of Control universe.
Kipling's writing influenced other science fiction writers, most notably the "Dean of Science Fiction", Robert Heinlein, who became known for his advanced rhetorical and storytelling techniques, including indirect exposition.
The word incluing is attributed to fantasy and science fiction author Jo Walton. She defined it as "the process of scattering information seamlessly through the text, as opposed to stopping the story to impart the information." "Information dump" (or info-dump) is the term given for overt exposition, which writers want to avoid. In an idiot lecture, characters tell each other information that needs to be explained for the purpose of the audience, but of which the characters in-universe would already be aware. Writers are advised to avoid writing dialogues beginning with "As you well know, Professor, a prime number is..."