There are a few different theoretical explanations as to how Finned XWings (or any other moves) work, but this is possibly the simplest explanation.
Suppose the 1 in r8c1 was False. Then there would be an X Wing in the four * cells, and you could eliminate the 1's in r4c2, r9c2, r6c9 and r9c9. You can call these Potential Eliminations, or PE's for short.
Now suppose the 1 in r8c1 was True. Then the 1 in r9c2 could be eliminated. Since r8c1 can't see any other of the X Wing PE's then you can't deduce anything about them.
So, since the 1 in r8c1 can only be True or False, and either way the 1 in r9c2 is False, then it is False and can be eliminated.
So in general, look for the X Wing PE's and any that can see the fin can be eliminated.
Compare this explanation with Andrew Stuart's here
or Hodoku's here
to see how I did.