What does a ‘Context’ do on a note?

The main link on any note is the person/project/company that the note is created on.  You can then add a context to indicate a link to another record on the system.  When the note is saved, you get a clickable link to the contextual record on the note itself, but this is not referenced back from the contextual record.

The only exception to this is when adding a note to a person from within a company, opportunity or assignment list of people (‘assignment candidates’ for example).  In this case, the note is created against the person as normal, but the parent record you are on (the assignment, or whatever) is added automatically as a contextual link.  This allows you to see the note in the company/opportunity/assignment’s ‘Related data’ tab as well as against the person record.