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Lens speed
The speed of a lens is determined by size of the lens opening, known as aperture. The aperture controls the amount of light that reaches a digital camera sensor . 
The diameter of an aperture is measured in f-stops. A lower f-stop number opens the aperture to admit more light onto the sensor. Higher f-stop numbers close the lens opening so less light gets through. A lens with an f-number of f/1.8 has a larger aperture than one with an f-number of f/4.5.
The aperture, or aperture range, is indicated on the front of a lens.
Fast lens
A fast lens is one with a large maximum aperture; the larger the aperture, the faster the lens. A lens is called fast because the larger aperture lets more light pass through during a given time span. When more light falls upon a subject, pictures can be shot with faster shutter speeds .
The aperture of a lens can be reduced if desired by the user of a camera with manual and/or semi-automatic controls. The process of reducing the aperture size is called stopping down. It’s important to note that a lens is usually not at its sharpest when wide open, nor when stopped down too much.
One interesting effect of using a large aperture is it greatly reduces the depth of field in an scene. This is very useful to isolate a subject from the background such as when taking portraitr and some marcro shots. A photographer desiring a large depth of field (for instance when photographing landscapes) will have to stop the lens down by using a smaller aperture.
Photographers who do a lot of low light photography prefer fast lenses.
Slow lens
A slow lens is one with a small maximum aperture, such as F/4.5. A slow lens lets less light pass through towards the sensor, and exposure times will be longer.
Longer zoom lenses are generally slower and have an aperture range. They are slower at the telephoto end of zoom and faster at the wide end.
A slow lens delivers a deeper depth of field. The same is true for a fast lens sopped down. A deeper depth of field can be desirable depending on the visual effect a photographer wishes to capture in a give scene.
Slow lenses less expensive than fast ones.
