A need is something that you must obtain in order to satisfy some want that you may have. You may be thirsty and so you'll need a glass of water to quench your thirst. In English we would never say that I have a requirement of a glass a water. We wouldn't say it that way because it's not required that I get a glass of water to survive because if it were, there wouldn't be people dying of thirst everyday!
But, to switch the words around a little bit more, you could say that a requirement of appeasing your thirst is the glass of water itself!
This is tricky but the bottom line is this: the word requirement is used in formal language specifying something demanded of a person in accordance with certain fixed regulations. The word need could be considered an urgent want and is used more in more colloquial (day-to-day) usages.
Hope this helps somewhat even though I know it may be a bit murky!
Suite aux excellentes explications de dookie418, je ne puis ajouter qu'une chose : pour traduire cela en Français il faut une phrase et du contexte. Ces mots peuvent avoir par exemple des significations précises dans un texte juridique ou dans un contrat, qui ne peuvent pas être traduite comme cela en l'air.