Why we use past tense in reported speech

David said "I am eating pizza."
David said he was eating pizza. 

The sequence of tenses as it is known in Latin classes is a way of dealing with reported speech.  Hearsay may not be admissible in court but in everyday English usage, we use it all the time.

Now all of you probably know how this works.  Someone says something and then later you want to tell someone else (or the original speaker if they contradict themselves) what they said.

The tense of the main verb is absolute but the tense of the subordinate verb is not absolute but rather relative to the tense of the main verb.  

What does that mean?
It means what when we use "say" or "said" the tense is based on if someone is speaking now or already finished saying what they wanted to say.  In the example in the picture (sorry for bad handwriting) we see that David said he was eating pizza.  The original sentence has David using the present tense but the report of what he said changes it to the past.  This is because David has already finished speaking and we used "said" in the past tense.  Since BE is not in absolute tense but rather relative tense we do not report the exact tense that David used but rather we let the listener know if the action was happening at the same time as the speaking or if the action happened before the speaking.  In this example the speaking and the action were at the same time so we use the past tense in the of BE.

"I am eating pizza."

David said he was eating pizza.

English speakers have this grammar in their heads but usually never realize it.  If asked, most will not even know why they changed the tense and will have to think about it for a while, as is the case with all interesting grammar.  It should be noted that many languages don't work this way and our way of doing things might seem odd, or even a lie. This fact of English usage can also be used for comical effect.

Tibadeaux:  Ah, man look at that girl.

Boudeaux:  What girl?

Tibadeaux: Dat girl over dere.  She hot.  I'm gone go talk to her.

Boudeaux: Good luck man.

Tibadeaux walks over to the girl and talks for a bit.  Then comes back.

Boudeaux: So?  How'd it go?

Tibadeaux:  No go.  She said she was married.

Boudeaux: That would't stop me.  If she was married then she ain't married no more.

Obviously Boudeaux thinks the tense is absolute and that the lady in question is no longer married, taking Tibadeaux's words at face value but that is probably not what she said.  Tibadeaux meant to tell his friend that her being married and her telling him she was married were at the same time and it is unlikely her husband died in the short time it took Tibadeaux to report this to Boudeaux.

This joke is comical because when we see Tibadeaux's report, we immediately understand that the woman is still married but when Boudeaux acts like an idiot and assumes she is no longer married because a past tense verb was used we instantly understand that he is being stupid but also we notice that we had not noticed the switch in tenses before.

So we use the past tense to say that something is happening at the same time as "said" but what if something happened before it was said.  In this case we need to go more in the past than the past tense to let the listener know that it happened before it was talked about.

I ate the pizza.

David said he had eaten the pizza.

Now it would strictly speaking not be incorrect to say "David said he ate all the pizza" if it was a very recent thing or some other instances but usually we would want to change "ate" to "had eaten" to push the verb more in the past so that it precedes "said".  In this way we let the listener know in what order the actions happened.  Eating first, then talking about it.