Free indirect discourse is a writing technique often employed when an author uses third-person limited narration. For the best explanation, I offer three examples (shamelessly gleamed from an AP English handout):
Indirect discourse:She thought she would stay there the next day.
Direct discourse:She thought, "I will stay here tomorrow."
Free indirect discourse:She would stay here tomorrow.
The point of free indirect discourse is to make the third-person narrator's voice take on the qualities of the character he/she is speaking about. The narrator becomes less detached, and his/her emotions more ambiguous, as the author switches between the three styles of narration.
Some examples of authors that use free indirect discourse:
Gustave Flaubert, Madame Bovary
Ernest Hemingway, "A Clean, Well-Lighted Place"
Stephen Crane, The Red Badge of Courage
These writers are all realists (except, possibly, Hemingway) and from what I've read free indirect discourse seems to be a favorite style of that particular group. Because their works dealt with characters and emotions, rather than outrageous plots (unlike the Romantics, who the entire realist movement seems to be a reaction against), this narration style allows the author to maintain his/her third-person voice while relating the emotions of the character.