Basically, a hymen is a very thin layer of skin - like tissue on
the inside of the vagina (hmm...how many of U out there REALLY use
this word?) just past the major and minor libia, which is the outer
most and not so outer most 'vaginal lips' covering that area.
No, I do not know why the hymen is there, eventhough I can
guarantee all that is certainly wasn't created by God for guys to
tell if their brides to be were virgins!!! 
What is certain is
that a whole range of activities can easily tear the hymen...from
something as simple as doing (real by definition of a
physiotherapist that is) stretching exercises to riding a bicycle
to little girls running around vigorously at the
playground!!!
As for your question, technically, yes, masturbating can tear a
hymen if there's any intrusion into the vaginal channel, or if
there's enough stretching, trashing and writhing about.
I wanted to say something earlier like go check a good biology
book, but then realise that a bio book won't really tell you much
simply because in biological terms, the difference between a torn
and intact hymen has NO health concerns or biological importance
whatsoever!!! The only importance given to a 'torn' or 'untorn'
hymen seems to be for the totally ridiculous judgement of whether a
girl is still a virgin or not, just to satisfy whatever male
pride/ego needs there be!
The FINAL nmessage to all girls out there: If you wanna mustabate,
and enjoy doing it...just be sure to wash your hands carefully and
enjoy yourselves!
