In Java "this" is always the current object - the one whose context the current method is executing in. The Thread constructor takes an instance of Runnable as its parameter, so "this" must be an object whose class implements the Runnable interface (which consists of a single run method). When the thread is started it will call the run method for the "this" object.
Java programmers are very pedantic - they have to be. You said
"I am wondering what the 'this' in the following code refers to ... I believe that it refers to the run method".
So technically that's false, even if you did have the right idea.
Anyway, mark this thread solved?