Free Indirect Discourse is a narrative structure that allows the reader to feel he/she is in the place of the character. In short, the reader becomes the focalizer, as well as the character. I will give you some examples because I think you should be able to distinguish the FID from the others Discourse features: Direct Discourse (DD) and Indirect Discourse (ID). Take the tense-scheme:
DD: He said: "I love her"
ID: He said he loved her.
FID: He loved her.
Questions, and here is where FID becomes so effective:
DD: She asked:"do you like me?"
ID: She asked if he liked her.
FID: Did he like her?
In the whole FID helps to make the text more realistic, or using a term introduced by Aristotle, mimetic - to create "the effect of the real" (being as realistic as possible.)