There was a time when the only measure Google had for relevancy of a page to a given search term was keyword density.

But keyword density was easily manipulated through the practice of keyword stuffing.

So Google moved away from keyword density and began looking at LSI keywords.

The reasoning was this:

A legitimate page about ‘Apple computers’ will likely contain a lot of other words and phrases that are related to Apple computers (such as ‘apple stores’, ‘apple iphone 5’, ‘apple new ipad’, ‘apple stock price’, ‘discount computers’).

On the other hand, a keyword-stuffed page about ‘Apple computers’ will probably just contain that one keyword, repeated over and again.

So latent semantic keywords provide Google with a way to differentiate between content that deals with a topic in depth, and content that has been optimized for the search engines by keyword stuffing.