What does Relevancy mean in SEO?

When a user searches 'keyword X' the first consideration a search engine must make it which pages on the internet are relevant to that search.

It will look through its vast index of web pages using an array of tools such as:

• Which pages contain the phrase 'keyword X'?
• Which pages give weight to the phrase 'keyword X' because it is in their title, url and the body text?
• Is the content of each page I have selected genuinely about 'keyword X' (see Latent Semantic Indexing)

Once it has this selection of pages it needs to order them in some way and for that it uses Authority.