What does Semantically Related Words mean?
These are words which mean the same thing or nearly the same thing. For example:
When search engines crawl a page and try to decide what the content is about they are aware of Semantically Related Words and so can take this into account.
We can see this in action if we do a Google search for "~bicycle"
When creating the content of a page it is important to understand that if you wish to rank for "bicycle" you need to include it on your page.
However if you include it, and Semantically Related Words, too often there is a chance you will be penalized.
Hence if you mention "SEO" and that makes up 6% of your word density and then you mention "Search Engine Optimization" and that makes up 6% and "Search Engine Promotion" makes up 6% some search engines may conclude you are using basically the same word 18% of the time, you are spamming and you deserve to be penalised.
On a similar note you should also be aware of Latent Semantic Indexing