A 'relief teacher' is another term for a 'supply teacher'. i.e. it's a teacher who is brought in to cover the duties of a teacher who is temporarily absent from their post (or to fill in between the appointments of permanent teachers).
The term is probably more frequently used in the USA than it is in the UK. However, it's similar to the usage of the word 'relief', in this country, when a shift worker says "I can't knock off until my relief arrives".
Also, some of us are old enough to remember that when one trolley bus broke down, the one which eventually turned up to replace it would simply bear the word 'Relief' on the destination blind. (i.e. it was 'filling in' for an absentee, in the same way that a relief teacher does).
Chris