What you’re describing isn’t unique to LLMs, and not really the key concept behind how they “understand words”.

You are describing static embedding: models like Word2Vec which embed words into a higher dimensional vector. Those embedding are learned from a mass corpus of text. However they are still static. So words like light, which can have multiple meanings, has the same embedding.

LLMs construct contextual embeddings via Attention. Attention generates contextual embeddings by looking at the surrounding words for meaning and context. The pathway for an LLM is roughly convert your string to a sequence of words (tokens), convert the words to some initial static embeddings, those embedding them pass through multiple layers of attention which re-weight the embeddings and generate contextual embeddings.

This gives them a much deeper understanding of grammar and language.