I have a book that puts very nicely what responsibility is, but it has a copyright on it, and I'm a stickler for keeping copyrights, if I know about them. This link, Teaching Responsibility, has some wonderful things to read which will help leaders be better able to explain and guide children into understanding Responsibility.
Demonstrate the importance of doing your part with a 3-legged stool. While it is possible, with extra effort, to sit with only one or two legs, all legs are important for stability.
Activities could include a trust walk or playing a game where each team or person has a responsibility that only he is allowed to perform. For instance, teach the positions of soccer, basketball, baseball, or football. You could build something, but each team builds a part, and then it gets put together. Teach them to take pride in doing their best with the responsibility they have been given, and how good it feels to do one's part in a group.
Ask what's important to them. Peace? Winning a game? Getting their turn? A clean house? Explain that taking responsibility is doing what they can to make these goals come to pass. If they want a turn, they need to let others have a turn. if they want to win a game, they need to practice at home as well as at team practice.
Have everyone bring 3 pieces of small trash. Have them walk around a small yard and nonchalantly drop each piece of trash around the yard. When everyone's finished, have them look at the difference only 3 pieces of trash makes. Then clean up the yard and throw away the trash properly.
Take responsibility for your corner of a clean world. Have each boy weigh the trash in their house for one day, then times it by 356 for a year. Visit a local dump and recycling plant. Talk about how to recycle.
Talk about the responsibility of their teacher or mother or coach or milking a cow. Then discuss what would happen if they did not take their responsibility seriously. Talk about what responsibilities the boys have at school and at home. Talk about the effects of their being responsible or not responsible.