Responsibility refers to the duty of having authority or control over something or someone. If you are responsible for something, you will be held accountable for the outcome of what comes from it, as this was your duty.
For quality management systems it is important that you take responsibility for your actions. This will show that you are serious about the job at hand, and will demonstrate integrity and ownership.
Most organisations have built-in responsibilities, whether these be related to their employees, customers or society at large.
Being responsible for things is hard to avoid, and the more your organisation owns this responsibility, the better off they will be.
In particular, organisations have a responsibility to ensure the health and safety of their employees at work. If an organisation chooses to ignore this responsibility for any given reason, the consequences for them could be catastrophic.