Necessary, inescapable, and non-negotiable, a requirement is something that must be done, like the dishes. Speaking politely to your grandparents may be a requirement of living in your parents' house.
Requirements can be imposed by an authority. For example, in college, it is usually a requirement that you study math, English, and history, before you go on to get your degree in underwater basket weaving. We can also speak of the requirements of a living system: your body requires water to stay alive; light is a requirement of photosynthesis.