My question isn't about the meaning and usage of it, but rather how it means what it means as I don't quite see it grammatically. For example, I can grammatically understand the usage of 心に残る、耳に残る and other phrases, but when I look for definitions of 印象 none of them refer to a physical or abstract "location". Is this just me misunderstanding how に残る is being used here or can someone else clarify this?
印象 in 印象に残る means "impressions" in the sense of memories of a memorable experience.
残る means "to remain, to stay behind, ..." and in this phrase doesn't refer to remaining in a physical location, but if you like to think of 残る as physical you may think of its use in 印象に残る as idiomatic. (Of course, 耳に残る doesn't mean you've got something in your ear.)
印象に残る then means "to be unforgettable, to stay in one's mind", similar to 心に残る "to be unforgettable, to stay in one's heart" where the difference is that the memory is not related to an emotion (which would be 心), but to a (say, visual or phenomenological) impression (that's 印象).