First and foremost, we need to know the meaning of responsibilities. Generally, responsibilities define as something that is our duty and need to be solved. In Islam being responsible is very important. Quran and Hadith also did mention about responsibilities several times.
To start with, by being responsible we are able to be a good servant to Allah. That is just so clear and Allah did mention in Quran in Surah Al-Isra' verse 23 [17:23] which means "And your Lord has decreed that you not worship except Him."
Thus, from that, we know that Allah sent us to the world with only one purpose which is to worship and obey His commands and it is our responsibilities to try our best in worshiping Him in order to gain His Rahmah. To mention some of the responsibilities that carry by every Muslims' shoulders are performing prayer five times a day, fasting in the month of Ramadhan, and even having to keep our physical and mental health are also our responsibilities as those are all belongs to Allah.
Being responsible also able to build a strong relationship. Other than that, this value will make one person to be able to become a leader. It is even is a must for a leader to have this character to lead one's organization effectively. In the other hand, by being a responsible leader it also can develop our personal growth, rationality and wisdom. And the last point is able to contribute to the society. Social responsibility means that individuals and companies have a duty to act in the best interests of their environment and society as a whole. Thus, all the community members can live peacefully.