“A person may cause evil to others not only by his actions but by his inaction, and in either case he is justly accountable to them for the injury.”John Stuart Mill · Despre libertate · 1859 · capitolul IV
Moral responsibility covers both action and inaction when you have the power to prevent harm.
Mill extends moral responsibility beyond actively committed acts. Doing nothing when you have the power to prevent harm is as blameworthy as directly causing it. The mechanism is simple: omission can be a conscious choice. For example, if you see someone drowning and do not throw a lifebuoy, you are morally (and sometimes legally) responsible for their death, just as if you had pushed them.
Why it matters This principle is essential in professional and civic ethics: passively witnessing an injustice makes you complicit.