In a lot of music sheets, I've seen that they mark the end of the song with 'Fine'
What does 'Fine' mean? And why is it used to mark the end of a song?
Because it means "the end" in italian. Remember that a lot of terms in classical music are in italian: rallentando, staccato, legato, etc.
Fine pretty much means the end of a piece. In piece you used for your example the end is pretty obvious, but some pieces of music will end in the middle after a D.S. al Fine.
In this example you can see the end of the piece is not where it would usually be. D.S. al Fine itself means go the Segno and play to the Fine. The Fine is used to say where the ending actually is.
Italian for "finished". standard notation text is usually in Italian per the standard ages ago.
So No more places to hop to. End of song.
There is no point or reason for putting 'fine' at the very end of a piece. It's obvious because of the double barline - and nothing following. However, the place it will be needed is where there is a DC or DS al Fine, which may well occur not at the last bar written, but at a bar somewhere else in the piece. Yes, there will be a double barline there, but in order to establish an absolute end, the word 'Fine' appears at that point.
"Fine" right at the end of the piece means two things: a) there is no ultimate reprise into the beginning/chorus: when the piece ends, it ends here. b) it is explicitly not "attacca": the next movement is not commenced in one flourish.
My understanding leads me to believe 'fine'(in the musical sense) means 'all stop' which is not at all superfluous, yes?