LSI means that a search engine tries to associate certain terms with concepts when indexing web pages. For example, Paris and Hilton are associated with a woman instead of a city and a hotel, Tiger and Woods are associated with golf.
Latent Semantic Indexing (LSI) is a statistical information retrieval method which lets you find relevant information not by simple keyword match, but by recognizing the "theme", the "topic" of a given document, in our case a website (Do I hear echoes of "topic distillation"? http://tinyurl.com/3wucm ). What's more, the document does not even have to include the keyword. LSI will get the "meaning" of the page and find it anyway. LSI is even capable of finding relevant pages in *other* languages.