I think this article is one of the best I've seen which describes LLMs in an accessible way without dumbing it down to the point where it's unhelpful: "Large language models, explained with a minimum of math and jargon"
One thing that might help you is to understand that LLMs store their 'knowledge' as vectors in a 'high-dimensional' space. As an example, here's a vector representation of 'cat':
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The distance and mathematical relationships between vectors is an essential part of how an LLM's abilities emerge.
This is likely an over-simplificiation but the way I think about it (I may have read this) is that prompts help orient the LLM context within its vector space. Prompt engineering is essentially finding ways to shift that context to a place in that vector space where it can produce better (or worse, depending on your goal) results.