In photography, aperture (also called f-number) refers to the diameter of the aperture stop (the stop that determines the brightness in a photo at an image point). Shutter speed on the other hand, is the total amount of time the shutter of the camera is open.
edit Function of Aperture vs Shutter speed
The aperture and shutter speed together control the amount of light reaching the image sensor (or film) of a camera. The degree of the sensor's exposure to light determines the brightness of the picture.
If the aperture (diameter of the aperture stop) is small, the depth of field (i.e. the distance range over which objects appear acceptably sharp in the picture) is larger. So all objects at varying distances from the view finder will be in equal focus. So the subject matter may be at a greater distance from the plane of focus and still appear in focus in the photograph.
The shutter speed controls the length of time that a camera's shutter remains open. So in effect, it helps the aperture restrict the amount of light that is allowed to reach the object. The impact of shutter speed is most prominent when photographing moving objects. Images taken with a lower shutter speed are blurred and invoke a visual sense of movement. A higher shutter speed allows clear images that are great for capturing specific moments in time e.g. a crisp picture of a football player in mid air.
edit Units for specifying shutter speed and aperture
Aperture is also called f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture). It is a representation of the diameter of the aperture stop in terms of the focal length of the lens. In other words, the f-number is the focal length divided by the "effective" aperture diameter. It is a dimensionless number. Standard ways of representing aperture are in sequence (f/2.8, f/4, f/5.6, f/8, f/11, f/16, etc.).
The agreed standards for shutter speed are 1/1000 s, 1/500 s, 1/250 s, 1/125 s, 1/60 s, 1/30 s, 1/15 s, 1/8 s, 1/4 s, 1/2 s, 1 s.
edit Correlation Between Shutter Speed and Aperture
Aperture and shutter speed together determine exposure. Exposure is measured in exposure value (EV), also called stops. Multiple combinations of shutter speed and aperture can give the same exposure: an exposure with a shutter speed of 1/250 s and f/8 is the same as with 1/500 s and f/5.6; or 1/125 s and f/11. Halving the shutter speed doubles the exposure (1 EV more), while doubling the aperture increases the exposure by a factor of 4 (2 EV).
This video explains the definitions of Aperture, ISO and Shutter Speed:
The following video provides recommendations on what shutter speeds and apertures to use:
And this video offers more recommendations on ISO settings, aperture and shutter speed:
The word aperture is derived from the Latin word apertura which means an opening. Shutter was used in reference with photography in 1862 and meant a device for the opening and closing of the aperture of the lens.