Initiative is one of the skills they will probably like, along with responsibility of leadership.
My advice would be to take the initiative and think about what will be beneficial. Don't just do it because you think it will look good, do it because you will enjoy it and better yourself because of it.
For example, I enjoy football. This requires a bit of responsibility, but I decided to run for captaincy at university. 2 birds with one stone. Leadership & activity in something I enjoy doing.
What responsibilities do you have at work? Day to day things? I'm currently in an office job just earning some money while I prepare. It's mundane, but I have responsibilities. Little ones, but they are ones I'm expected to complete well, and with integrity - such as invoicing and liaising with customers