Latent Semantic Indexing (LSI) refers to the concept of identifying patterns in an unstructured string of words and defining relationships across words that display similar ideas.
Therefore, LSI keywords refer to those words that display similar ideas e.g. using Tesla and Elon Musk in a content piece indicates an idea around electric cars.
By using multiple LSI keywords that relate to the focus keyword, one can build context into the content thereby sending strong signals to Google about the search relevancy of the content.