What is oxygen's role in the electron transport chain?

There are a lot of parts and pieces involved in the electron transport chain, but with respect to Oxygen, the simple answer is Oxygen is the place where the electrons go, it i sthe thing that gets reduced.

I'm not going to link to all the membranes and chemical reactions, but rather just refer to something simple like a carbon in a typical fat.
`-CH_2-` this is what a carbon in a fat looks like (in general).
As that carbon sits now, it has a ~ -2 oxidation state.

When you exhale that carbon as `CO_2` (after cellular respiration and oxidative phosphorylation, etc), the C has a +4 oxidation state.

That means for the Carbon:
`C^-2 = C^"+4" + 6e^-`
Those 6 electrons have to go somewhere. And they go onto Oxygen!
You breath in elemental `O_2` with a zero oxidation number. That carbon above turns into a `CO_2` and basically 1 water, `H_2O`
So that Carbon needs to get rid of 6 electrons...and in `CO_2`, each Oxygen has a -2 oxidation state (from zero to -2), and the water oxygen has a -2 oxidation state (from zero to -2). So when that Carbon in the fat gets oxidized and you breath it out as `CO_2`.
The place were those 6 electrons went is onto the `O_2` that you breathed in (and breathed out as `CO_2` and maybe some water (simplistically speaking)