Latent Semantic Indexing is a very technical concept, way above my pay grade! If you really want to get down into the weeds on it and get your head spinning visit this link.

For DIY-SEO purposes here’s what you need to know.
Latent Semantic Indexing is basically a technology that Google uses to analyze the content on your pages searching for OTHER RELATED words that support your main keyword or keyword phrase.
These “other” related words help Google determine RELEVANCY for that page, and that’s what Google wants – to make sure your page is relevant to the search being performed.
When Google finds these related words on your page it helps your page get better rankings. Think of it as a “thumbs up,” for your targeted keywords/phrase.
Google uses LSI as a way of checking whether your page content is genuine, or just stuffed with random keywords in an attempt to improving rankings. Think of LSI keywords as words that would be mentioned naturally in a genuine conversation about your primary keyword/phrase.
Say your keyword phrase is New York City Wedding Officiant. Some of the LSI related words that should ALSO be included on your page might include: wedding minister, wedding planning, wedding vows, ceremony, commitment, wedding rings, wedding ceremony location, Brooklyn, George Washington Bridge, Big Apple, maybe even Empire State Building and the acronym NYC.
Tomorrow: DIY-SEO continues with page-title and description meta-tags (VERY important).