You can get as detailed as you want in defining it.
Here is what Wikipedia says.
cLSI keywords relate to the primary keyword we are targeting. You can help with the SEO of an article by including these in your text in a natural way.
Here is a latent semantic indexing example....
You have a blog on dog training. LSI keywords that would be natural to find in an article would include cats, puppy, pets, housebreaking, etc.
Google has algorithms that are so sophisticated today they actually track this stuff and include them when ranking your content for keyword variations.
I do not worry to much about LSI keywords. I try to write naturally. I do attempt to include keyword variations.
Let Google Help
You can use the free Google Keyword Planner Tool to do keyword research. You should have a long list of keywords for you blog anyway.
Use it to find LSI keywords as well. Search for your primary keyword and let Google give you results. Scroll down and find the area for keyword ideas. This is the list of LSI keywords you can choose from that Google likes.
Here are 2 good articles you should read.
How to Find LSI Keywords and Implement Them for SEO
How to do Long-Tail Keyword Research for SEO
Related Video: Understanding Latent Semantic, Google Indexing