Python has classes for Tkinter variables StringVar(), BooleanVar(), etc. These all share the methods get(), set(string), and trace(mode, callback). The callback function passed as the second argument to trace(mode, callback) is passed four arguments, self, n, m, x.

For an example of a BooleanVar() these appear to be '', 'PYVAR0', 'w'.

The third argument x appears to be the mode that triggered the trace, in my case the variable was changed. However, what is the first variable that appears to be an empty string? What is the second, if I had to guess I'd say some internal name for the variable?

The first argument is the internal variable name. You can use this name as an argument to the tkinter getvar and setvar methods. If you give your variable a name (eg: StringVar(name='foo')) this will be the given name, otherwise it will be a name generated for you by tkinter (eg: PYVAR0)

If the first argument represents a list variable (highly unlikely in tkinter), the second argument will be an index into that list. If it is a scalar variable, the second argument will be the empty string.

The third argument is the operation, useful if you are using the same method for reading, writing and/or deleting the variable. This argument tells you which operation triggered the callback. It will be one of "read", "write", or "unset".

Tkinter is a python wrapper around a tcl/tk interpreter. The definitive documentation for variable traces can be found here: http://tcl.tk/man/tcl8.5/TclCmd/trace.htm#M14. Though, this only documents how the internal trace works, the tkinter wrapper sometimes massages the data.