Moisturising protects the skin from the exterior environment - wind, sun, pollution, cold, or drying air conditions can age the skin prematurely.
For dry skin, rich moisturisers will keep it supple and elastic. For oilier skin, only a light moisturiser is needed, otherwise the pores can become clogged and heavy. Some moisturisers have been produced to tailor to all skin types - you may find the need to apply more or less according to your skin's needs.
There is some debate over whether you need a separate day time and night time moisturiser - I feel it comes down to your personal preference. Try it for a week and listen to your skin.