What are these characters from the OS X keyboard? I've never seen these characters before and never seen them in action either.

Does anybody know what they are and what they're used for?

Maybe somebody has this drop of trivia lying around...

Option+Shift+6


  ﬂ


Option+Shift+5


  ﬁ
These are U+fb01 and fb02, Latin Small Ligature Fl and Fi.  They are in Unicode really only because they were contained in legacy 8 bit character sets like MacRoman, but should no longer be used for anything.  In modern technology such ligatures are created by fonts on the basis of the underlying codes for the separate characters, which is what should aways be input in place of option shift 5/6.