This quote was made by Winston Churchill, an orator who knew the courage it took to speak and also to listen.
The quote "COURAGE is what it takes to stand up and speak and what it takes to sit down and listen" basically means it takes courage to do the right thing (decide when to stand up and speak and when to sit down and listen).
Courage does not always mean standing up and speaking, sometimes it entails sitting down, questioning your own opinions and beliefs and listening to other people speak.
In school it sometimes gets boring to listen to the teacher all the time, and work with the same person over an over againe. Group work is the best solution for this.