First Take:  In story-telling, the act of presenting the thoughts of a given character in such a way that those thoughts seem to blend with the voice of the narrator (or, in this case, the journalist). 

Deeper: Free indirect discourse is a deeply technical term in narrative theory, and there are many nuances accompanying it. For instance, perhaps we read something like this in a work of narrative journalism:  

Reggie thought his sister was dissing him; she had never had his back in the past, even when Pops gave him an ass-whooping right in front of his boys on 14th Street.

Some thinkers will say that such a sentence is not meant to be interpreted as Terry directly speaking: there are no quotation marks, and he is being presented in the third person. Rather, it is thought, the passage represents the author indirectly recounting what Terry was thinking, and in part using some of the vocabulary the journalist might use, too. Moreover, even though people don’t usually “think” in complete sentences this way, as readers we often accept that they do. Nevertheless, we should call this an “indirect” rendering, but also “free” in the sense of being freely remade by the writer.
          With long-form journalism, however, the difference from fiction is considerable. As readers of narrative journalism, we commonly conclude from the passage above that the journalist has either asked Terry what he was thinking or–and here’s the tricky part–inferred what he was thinking and feeling. Thus, free indirect discourse serves a double role as “internal thought” and as a form of attribution (see this glossary entry).  This additional function is one of the reasons this is called “discourse”–meaning, in part, that the passage implicitly reflects a back-and-forth understanding or conversation between the journalist and the subject. As such, free indirect discourse is one of the ways (as I suggest in Chapter 3) that a journalist can claim to construct sympathy and “common cause” with a subject. Nevertheless, readers should take note of vocabularies and assumptions that could not have been held by subjects–in that case, the journalist’s hand can be detected.