“indirect speech: The reporting of something said, thought, etc. with deictic and other units adapted to the viewpoint of the reporter. E.g. He said he would bring them might report a promise, originally expressed by the utterance ‘I will bring them in.’ But the person who made the promise is someone other than the reporter; hence, in the reporting, original I is changed to he. Also the promise was earlier than the report; hence, in addition, will is changed to would. With these adaptations, he would bring them is an example of, and is said to be ‘in,’ indirect speech.”
Excerpted from: Matthews, P.H., ed. The Oxford Concise Dictionary of Linguistics. New York: Oxford University Press, 2014.