A tremolo arm is what allows one to use a tremolo. A tremolo is
a mechanism in a stringed instrument that allows changing the pitch
of all the strings simultaneously.
The major drawback of a tremolo is that large amounts of use
will stretch the strings and throw the instrument out of tune,
requiring the player to have to continually retune the instrument.
The idea behind the Floyd Rose brand tremolo is to alleviate this
problem by locking the strings at both the nut and the bridge. More
details on the Wikipedia page here:
http://en.wikipedia.org/wiki/Floyd_Rose