According to Immanuel Kant what is the difference between duty and inclination and why is it important?

For Immanuel Kant, the moral value of an action has nothing to do with what a person does.  Actions themselves are not good or bad.  In addition, the results of the action do not determine whether it is good or bad.  The only thing that determines whether an action is good or bad (or morally indifferent) is the motive behind the action.  This is where the difference between duty and inclination comes in to his thinking.

For Kant, inclination consists of things that we desire.  If we act because we want something, we are acting from inclination, regardless of whether the action seems to be good or bad.  For example, if I stay after school without pay to help a group of students, I might be acting from inclination.  I might be doing that because I want the students to think well of me.  In that case, I am acting to try to achieve something that I desire.  As another example, let us say that I spend a lot of time with my kids, giving them attention and love.  I might be doing this from inclination because I enjoy being with them and I want to feel their love in return.  Also, I might be doing it from inclination because I want them to grow up and get good jobs or because I want them to be smart and to make their teachers think that I am a great parent.  In each of these cases, I am acting because I think my action will get me something that I want.  This is inclination.

Duty, by contrast, consists of things that we know we should do.  If we act because we know that it is the right thing to do, we are acting based on duty.  If I stay after school with my students because I know I have a responsibility to help and support them so they can succeed in life, I am acting from duty.  If I spend time with my kids because I know I should (even though I would rather be watching sports on TV) I am acting from duty.  Kant says that only actions motivated by duty are morally valuable.  If we act based on inclination, our actions are, at best, morally neutral.

The different between duty and inclination, then, is the difference between what we should do and what we want to do.  This difference is very important because Kant says our actions are only morally good if they are motivated by duty and not by inclination.