What is "backshifting", as applied to English grammar?

I saw this term, backshifting, in an answer to another question, that was not endorsed by the community:

[T]he process called backshifting...signal[s] that the speech is not direct/quoted but rather it is indirect/reported.

That sounds very interesting, but unfortunately, I can't be sure of if this given definition is correct, as it is found in a downvoted answer.

So: What is backshifting, and how does it apply to English? As always, plenty of examples are requested!

Answer

I think what Dan meant was what happens to direct speech when you turn it into indirect speech; this is especially notable when the indirect speech is subordinate to a sentence in a past tense:

She said: "I will tell him that you
lied". (Direct speech, no shifting.)

She announced that she would tell him
that you had lied. (Indirect/reported speech, tenses shift.)

Because the tense of the main clause is in the past ("announced"), the finite verbs in the reported/indirect speech shift back in time: "will" becomes "would", and "lied" becomes "had lied".

So "I" becomes "she", because I decided that it was "she" who was announcing her own intentions ("she said" in the first example). You could say "she announced that I would ..."; it would just describe a different situation. That all depends on who's who and who's talking.