It's important and it's there for a reason. You have to respect this rule if you want to get over your ex. especially if you are having a hard time with the whole breakup thing and can't figure out how to move on.
When you see your ex your feelings instantly start to work themselves up into a panic and whirlwind which then affect your thoughts.
You need to let your brain have some time to figure things out for itself without your feelings about the other person affecting its rationality.
This is really the single biggest thing you can do to get over your ex. Avoid contact with them and let your mind heal itself.
But this can be easier said than done sometimes.
What if you work with them? Go to school with them? Have common friends that you regularly both hang out with?
Well this is a little harder than if you never have to see them again but it's doable. Remember that you don't have to avoid them forever; you just have to give your mind and heart some time to heal.
I'm sure you know their schedule better than anyone and yours is probably pretty close to theirs if you are around them in outside activities quite a bit. So you need to work around their schedule and start making a new one for yourself.
It can be easy to avoid them and barely see them if you try. If you work together and they get to work at eight in the morning then you start to get there fifteen minutes earlier. If they normally walk down a certain sidewalk at nine then you avoid that sidewalk at nine. If you go to school together and they sit in the back left, you start sitting in the front right. Put as much distance between the two of you as you can. If there's no chance for zero contact than the distance will help you deal with the breakup the best you can.
And if you have the luxury of being able to avoid them completely until you are over your feelings then use that advantage you have.