Before to know “Latent Semantic Indexing(LSI) Keywords” you have to Latent Semantic Analysis. LSI refers to the keywords which are close and relevant to the keyword. A very popular example is Apple keyword. If you write about apple how will search engines know that you are writing about a fruit or a company? If you write about Apple which is fruit. Your post will have LSI keywords, test, red, vitamins, sweet, ambrosia which are LSI keywords for Apple fruit. However, if you write about Apple Incorporation the LSI keywords will be iTunes, iOS, macOS etc. which are LSI keyword for Apple Incorporation.
Latent Semantic Indexing Keywords and Search Engines-
Google Hummingbird search algorithm brought LSI to provide the most relevant content for queries. Further, also penalizes for keyword stuffing. Before this algorithm, the search algorithm used the number of keywords to determine the most relevant content. Which could be easily misused.
Latent Semantic Indexing Keyword and SEO-
For SEO you can not do a lot about LSI. However, you can avoid keywords stuffing. Furthermore, If you write long content length ( about 2000 words ) post in a natural way. You will be using LSI keywords automatically.
 Deerwester, S., Dumais, S.T., Furnas, G.W., Landauer, T.K. and Harshman, R., 1990. Indexing by latent semantic analysis. Journal of the American society for information science, 41(6), pp.391-407.  Dumais, S.T., Furnas, G.W., Landauer, T.K., Deerwester, S. and Harshman, R., 1988, May. Using latent semantic analysis to improve access to textual information. In Proceedings of the SIGCHI conference on Human factors in computing systems(pp. 281-285). Acm.