In a nutshell it's about having related words in your page text. If your page is about trainers, you will get more credit from Google if the page also contains symantically related words and phrases such as training shoes running sports etc, etc LSI has been around for a long time but hasn't played a major part in the Google algo, till now. Rumour has it that Google is now turning up the LSI knob.
As per the defination goes: LSI is a methodology involving statistical probability and correlation that helps deducing the semantic distance between words. It’s obviously a complex methodology but can be easily applied to understand the relation between certain words in a paragraph or in a document. This methodology is being used while indexing a page in the search engine’s database.
There was a recent article on it from the Entireweb newsletter... Check out www.entireweb.com/newsletter to see if you can get hold of one of the back issues - i believe you possibly can!
It's actually latent semantic indexing. Symantic is a company, and Analysis doesn't start with an I as far as I can tell. The short version is that you'll be indexed higher in the rankings if you deal expertly in the subject. The long version is at SEO2020.com. MR