Latent Semantic Indexing (LSI) is an indexing and retrieval method that uses a mathematical technique called Singular value decomposition (SVD) to identify patterns in the relationships between the terms and concepts contained in an unstructured collection of text. Best source Wikipedia.
Latent semantic indexing, other wise known as LSI, is not what is it is frequently claimed to be. It is not something that a webpage can be optimized for, so that it conforms to LSI standards. There is no such thing as LSI standards. In fact, latent semantic indexing cannot be described to a layman in simple terms.LSI cannot be used to improve your search engine listings since it is nothing more than a concept. A very mathematically complex concept, sure, but a concept nevertheless, and concepts cannot be used for tangible results. However, there is a guide to what Google are trying to achieve in the use of the words within the term. In the context in which it used, the word semantics here means the meaning of words, and specifically the meaning to which words are put, and what is being conveyed, in the way that the term is used.
All these explanations don't really help. LSI is Latent Semantic Indexing. For SEO purposes, it means adding related keywords of the main keyword (not synonyms) in a page/article to help Google determine what your content is about. It also strenghtens your page for your main keyword and helps you rank for more related terms.
LSI means technically you have to put the synonyms in the article that saves from keyword stuffing and help to target the keyword.