In simple terms, a fault model is a generalized abstraction (or model) of a particular category or type of an error.
The theory behind fault models is that if we can understand the root cause of a particular type of error that occurs repeatedly (a pattern of error) then we can probably design a test technique or tool to help us identify that type of error more efficiently and more effectively, or implement a tool or process to help prevent or reduce the occurance of that type of problem.
Of course, if you only goal as a tester is to find bugs, then understanding of fault models, or performing root cause analysis, or other defect prevention approaches may not be important.
I always wonder on how is the relevance of a Test Design Technique relavent to the AUT. I feel that if my understanding of Fault Models is feel definied, I might be able to better implement these test design techniques to my testing.
I have no idea. I think it's fairly arbitrary, just as many terms are in the SQA industry. I think we extract the core ideas from other industries (same with sanity and smoke testing) but the definitions within the industry vary widely. I don't think you'll really find anything documented on fault models as they relate to the SQA industry specifically. Names could simply be extrapolated from ideas of what you are attempting to do.
9 out of 10 people I prove wrong agree that I'm right. The other person is my wife.
An adaptation of a "fault model" (whatever) is the "Notes" column of a test script. If when writing the test you as test analyst think of ways in which some bug may manifest itself you might add these ways in the "Notes" column.
They don't define the test, but they can help someone who has had less time to think through the possible defects to recognise one faster.