Monitors are not just for playback and hearing what you are recording. They are there to reveal the truth about the sound detail. It is important that you have an acurate "picture" of the sound you are recording. You need to be able to tell if there are any harsh frequencies, noise or hum present while tracking. Not to mention that mixing on a good set of monitors will make sure that your mix sounds good on any system the tune is played on.
If you mix on a crappy set of speakers, you will end up EQing for that set of speakers. Then when you play your track on another system you will wonder why it doesn't sound right. If the monitors you have are fairly neutral, your mix will translate well to other systems.
Also, mixing on headphones is bad! Your brain alters the sound when wearing headphones and doesn't account for room acoustics and reflections.
Someone else is sure to explain that better than me!