Learn French: J'ai expliqué que le conducteur avait freiné parce qu'il pleuvait. - I explained that the driver had braked because it was raining.

Because this is reported speech introduced by a past tense verb (J'ai expliqué). If you were speaking in real time, you would use the passé composé: the driver braked (le conducteur a freiné). But since you are reporting it in the past, that action shifts one step further back into the past, becoming the plus-que-parfait (avait freiné).

Why didn't pleuvait shift further back in time like avait freiné did?

Pleuvait is in the imparfait, which describes ongoing background conditions. Unlike the passé composé, the imparfait does not change when you backshift in reported speech. It stays exactly the same because it is still just describing the background setting of the story.

Could I use chauffeur instead of conducteur here?

You could, but they have slightly different meanings. A conducteur is anyone driving a vehicle, while a chauffeur is someone who drives as a profession, like a taxi or bus driver. If you just mean an everyday person driving a car, conducteur is the best choice.

Why is it parce qu'il instead of parce que il?

The word que always drops its e and uses an apostrophe when the very next word starts with a vowel or a silent H. Since il starts with a vowel, parce que il must become parce qu'il.