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I need some help to interpret a sentence. I would like to know what "switch it off" means here for a native speaker. The girl here is thinking about how some people have the ability (which she doesn't have) to remember music and to always hear music in their minds. (The garage is the place where the girl works):

Whenever anything did get stuck in her head— a jingle from a television commercial, some popular tune— she found it claustrophobic and couldn’t wait for it to stop. When music was playing on a stereo or in the garage, she could tune
it out or switch it off if it got tiresome, but now she wondered if this was a shortcoming on her part.

Does "switch off" mean "turn off physically the stereo or the music", or just the mental action of ignoring it?

When music was playing on a stereo or in the garage, she could tune it out or switch it off . . .

Switch off is used literally to designate turning or flipping a switch to end the functioning of a machine or appliance. But it may also be used metaphorically of mental function: we might speak of "switching off" your attention to some phenomenon.

In your example, where actual music is being played, switch off is probably meant literally, since it contrasts with tune out, a similar expression (drawn from 'tuning' a radio to a particular channel) which today is almost always employed metaphorically.

PARAPHRASE:

When music was playing on a stereo or in the garage, she could ignore it or turn the stereo off . . .

I take it you understand the actual meaning of "switch it off", but you don't know what "it" refers to in this context? Truthfully, the sentence is confusing, even to native speakers. In the end we just have to make a best guess based on the overall point of the passage. It's more about good, general reading comprehension than any understanding of individual words.

Here the character is describing a personal trait where, once she gets something stuck in her head, she can't get it out. Because this trait is the focus of the passage, we can assume "it" also refers to the trait, or to the thing that is stuck in her head.

The author's use of "switch off" makes this even more confusing, because it's a physical action, and you would expect this apply to the actual stereo system. But again, in the context of the passage it makes little sense for the character to say she can switch off the music was playing -- instead it makes more sense to suggest that external, background noise can help her turn off the internal noise.

Alternately, the character is saying that she can tune out external background noise so it does not get stuck in her head, but again this is strange since she just said she "couldn't stand for it to stop".

So any way we read the passage, it doesn't really make sense. This is just poor writing, or at least poor editing since a professional editor should have caught this confusing passage and asked the author to rephrase.

If "switch off" was being used metaphorically in this sentence, the writer would not have included "tune it out" as an option. Tune it out and figuratively switching it off would be the same thing. This would make switching off a physical or literal action.