Halliday & Matthiessen (2014: 253, 254):
But there is one further option open to such clauses – an option that sets them apart not only from ‘material’ clauses but also from ‘relational’ ones. This option is the ability to set up another clause ‘outside’ the ‘mental’ clause as the representation of the ‘content’ of consciousness. … Here the ‘mental’ clause projects another clause (or combination of clauses) as a representation of the content of thinking, believing, presuming and so on; the projected clause is called an idea clause.