LSI keywords (Latent semantic indexing keywords) are used by the search engines to find and add synonyms for your keywords. This allows them to identify the proper content of your website, so it might then rank your site accordingly in the search results.
In the past, LSI keywords were not used for this purpose; the blogs appeared in the search results according to the keyword density in their content. This can be explained simply as if someone has mentioned a keyword five times in an article, then you need to use that keyword in the content at least six times to get the lead in the search results of a search engine. This fairly compromised the quality of the content and now is replaced by the latent semantic keywords.
LSI keywords are not difficult to understand. These are actually the words that are only used with a particular keyword to describe it more appropriately. It gives more wise idea to the search engine that to which specific content the person wants to gain access.
For example if the keyword for content is apple, it becomes quite tricky for the search engine to identify whether this apple is a regular fruit it is about the international "apple brand". Here is the place where these LSI keywords play their part. The LSI for the fruit, apple would be its taste, aroma. So, if these are also mentioned in the content with the keyword apple, it become easier for the search engine to understand that it is the fruit apple, then it ranks the site with such content properly.
It is quite interesting that these LSI keywords are not that difficult to know. If you search a keyword on Google, it spontaneously offers you a set of keywords that are actually latent semantic indexing keywords.