I saw the sentence in my book ‘each one represented a goddess’, and I felt I can delete the ‘one’ of the sentence. Can I, and why?
I think in all such contexts, each one is simply an optional "flourish" that doesn't really make any difference at all - but some people might think it adds slightly more emphasis.
Most dictionaries would probably give every one (two words, not the single-word form everyone = everybody = all people) as an exact synonym that can directly replace each. But note that regardless of whether or not the "original" included the word one, it's always required after every in such contexts.
I can't think of any context where it's necessary to include one after each, so my advice for learners would be to stick with plain each unless you want to be more emphatic, in which case you could express that using every [single] one (where including single adds even more emphasis, but note that each single one would rarely be idiomatic).