A moral imperative is a strongly-felt principle that compels that person to act. It is a kind of categorical imperative, as defined by Immanuel Kant. Kant took the imperative to be a dictate of pure reason, in its practical aspect. Not following the moral law was seen to be self-defeating and thus contrary to reason. Later thinkers took the imperative to originate in conscience, as the divine voice speaking through the human spirit. The dictates of conscience are simply right and often resist further justification. Looked at another way, the experience of conscience is the basic experience of encountering the right.
An example of not following a moral imperative is making a promise that you do not intend to keep in order to get something.
At what point do you follow what you know to be your own moral imperative? Is it when your parents are dead and therefore you have no further commitment to them? When you are ready to unfollow the culture and values to which you have been indoctrinated? When your children are no longer your number one priority and it’s worth risking their condemnation to break your own status-quo? When it means leaving your job, your career, and your only source of income?
It happens when your thoughts are screaming out for action and those actions can no longer be contained and must break free; basically it happens you have no other choice or else your sanity is at risk.