QUOTE(OneManBand @ Dec 23 2009, 08:31 PM)

If you're playing a solo instrument, the direction of the stem doen't really make any difference. As river said, it's usually used on vocal scores where two singers are at the same pitch.
But it is also helpful in contrapuntal music (e.g. Bach Fugues) to show that two separate contrapuntal lines have momentarily met at the same pitch. Having two stems gives each line visual continuity and makes it easier to read. Besides, if the second stem were not there then, for clarity, the composer would have to write in a rest to show that one of the voices has stopped.
Related to this, if you study piano scores you will find that very often the same note is shown in both the bass and treble clefs - poerhaps as part of the harmonic accompaniment for the LH, and part of a melody in the right. It is just the same - the note has two functions, but on a keyboard you can onl;y play one of it.
The point is that the music is not a set of instructions for physical actions to be performed to make sounds. It is a visual representation of musical ideas. One of those ideas is the melodic line, or multiple melodic lines going on at the same time. If you could not use the double stem you'd have to write the music in an expanded form over more staves.