LSI stands for Latent Semantic Indexing and is special SEO terminology for keywords that are semantically related to your primary keyword. More specifically, search engines look for words before and after your keyword that links together giving the keyword meaning. If the words before and after are popular and frequently searched then search engines know that the content must be relevant. LSI keywords are not just synonyms to your target keyword. They play a major role in determining the content relevancy of your web page and help search engines determine your ranking.
When Google and other search engines are performing their search, they look at some factors to determine which web pages rank higher than others. One important factor is the content relevancy of your page. If you are constantly reusing the same keyword on your page, search engines can identify this as redundant keyword stuffing. In the early days you could be penalized in your rankings, but modern search engines today understand and ignore this type of behaviour. LSI keywords can be used to reduce the amount of keyword stuffing, leading to a higher content relevancy score, and a higher ranking for Search Results.