Learn Italian: Mi ha spiegato come cantare il ritornello, cioè dove respirare. - He explained to me how to sing the chorus, that is, where to breathe.

This sentence features implicit indirect questions (come cantare, dove respirare). You can use a question word followed by an infinitive when the person performing the action is already clear from the main clause. Here, because he explained it to me (mi), it is understood that I am the one who will sing and breathe.

Could I use a conjugated verb instead of the infinitive here?

Yes, you could make it explicit by conjugating the verb, usually with a modal verb: Mi ha spiegato come devo cantare... dove devo respirare (He explained to me how I should sing... where I should breathe). However, using the infinitive is much more natural and concise for general rules or 'how-to' instructions.

What exactly does cioè mean in this context?

Cioè translates to 'that is' or 'meaning.' It is a combination of ciò (that) and è (is). Italians use it constantly as a filler word or to clarify and rephrase a statement. Here, it clarifies that knowing how to sing the chorus primarily means knowing where to take a breath.

Why is it Mi ha spiegato and not Me lo ha spiegato?

Mi ha spiegato (He explained to me) is used because the direct object of the verb spiegare is the entire following clause (come cantare il ritornello). If you used Me lo ha spiegato, the lo would mean 'it,' which is redundant since you are explicitly stating what the 'it' is right afterward.