
Bruce P. answered 04/10/20
20+ year college biology/genetics teacher; I want you to understand.
A short answer would be 'source, transport, conversion'. Let's look at what that means. We all 'know' that sugar is a fuel source, but why? WHERE is the energy in glucose? It turns out it's the electrons, or more correctly, in the state of the electrons. Electrons in C-H bonds are more energetic than those in O-H or C-O bonds, and sugar has many C-H bonds (and thus many energetic electrons). Pyruvate is just a 'piece' of glucose, so still has most of the energetic electrons from glucose.
To 'extract' or harvest the energy of electrons, they need to be taken to the mitochondria, which is basically a factory housing the machinery to harvest electron-power. NADH is 'given' some of the energetic electrons that are ripped from pyruvate (this is a multi-step process; pyruvate is broken into acetyl-CoA, and then electrons are pulled out during the Krebs/Citric Acid/TCA cycle). NADH then delivers these charged-up electrons to the electron transport chain.
The purpose of the electron transport chain is to CONVERT the 'power' of the electrons into a different kind of power--crowded protons all on one side of a mitochondrial membrane.
ATP synthase is like a waterwheel, except that instead of water, PROTONS flow through it, and the flow of protons drives the synthesis of ATP through the combining of ADP and phosphate. ATP synthase sits in a mitochondrial membrane and in order to get to the 'low concentration' side, protons must flow THROUGH ATP synthase, thus driving its internal 'wheel' and powering the synthesis of ATP