Latent Semantic Analysis aka LSA is not the same thing as Latent Semantic Indexing aka LSI. LSA is the basis for LSI. It is the result of LSA that leads to LSI.
LSA is not about replacing keywords with synonyms either. Just replacing keywords with synonyms doesn't make LSA show better results. The whole idea behind LSA is to determine whether the content is relevant to the topic at hand.
Take for example, you have a topic which says "Top Dog Breeds". LSA will parse your content to see if you are really talking about top dog breeds or you are just stuffing keywords and synonyms for keywords, purely for the purpose of fooling search engines into thinking that the article is about top dog breeds when in actual fact, it is just full of rubbish without any useful information about top dog breeds.
LSA is a tool based on mathematical formulas. It works with semantic groups of words. Semantics focus on the meaning of the words rather than the actual words themselves. So in the article given as an example above, it's not enough to just replace the word dog with, say, canine, pooch, mutt, etc. There has got to be other words which give the meanings related to dogs like, say, companionship, guard, watch, care, etc. And the words must be connected in a meaningful coherence.
In simple language, LSA just means that it's a way to see if your content is what it claims to be.