Despite the widespread use of the notion of moral intuition, its psychological features remain a matter of debate and it is unclear why the capacity to experience moral intuitions evolved in humans. We first survey standard accounts of moral intuition, pointing out their interesting and problematic aspects. Drawing lessons from this analysis, we propose a novel account of moral intuitions which captures their phenomenological, mechanistic, and evolutionary features. Moral intuitions are composed of two elements: an evaluative mental state and a feeling of rightness (FOR). We illustrate the phenomenology of the FOR with examples of non-moral and moral cases, and provide a biological and mechanistic account: the emergence of human reasoning capacities created a need for the co-evolution of a psychological system producing the feeling of rightness (the FORs). This system is triggered when we experience conflicting evaluations. The FORs renders evaluations resulting from rational deliberation less compelling than the evaluations produced by simple evolved systems. It thus facilitates optimal decision-making, preventing excessive interference by rational deliberation. Our account sheds light on why moral intuitions are so frequently experienced and why they are so compelling and resistant to argument. In addition, the account fuels interesting speculations about common metaethical intuitions.