The ability to do what needs to be done without being prompted by others or the willingness to take a fresh approach
These attributes are probably some of the most important determinants of success in any situation. Self-motivation is about your internal drive to achieve, develop and keep moving forward; it is what pushes you on to complete something when you feel like giving up.
Linked to this is initiative: This is about being proactive rather than reactive, spotting and taking advantage of opportunities as they arise and persisting in the face of setbacks.
It makes their job easier! Once a self-motivated person is familiar with the organisation or team objectives, they will get on and do what is required of them - and more - in order to meet and exceed those objectives. They are also more likely to be on the look out for, identify and take advantage of opportunities as they arise. This can have many benefits for the employing organisation such as new business opportunities or improved systems or processes.
This will be different for everyone so you need to identify what motivates you in order to provide examples during the application process, but in general, examples of when you have done something over and above the norm, or out of the ordinary, can be good to use.