The focal length of a lens determines its angle of view, and also how much the subject will be magnified for a given photographic position.
Focal length also determines the perspective of an image.
Longer focal lengths require shorter exposure times to minimize burring caused by the shake of hands.
The aperture range of a lens refers to the amount of light that the diaphragm can let inside the camera to reach the sensor.
Apertures are listed in terms of f-numbers (expresses the diameter of the entrance pupil in terms of the effective focal length of the lens; It is the quantitative measure of lens speed), which are marked on the lens.
On a camera, the f-number is usually adjusted in f-stops.
Each “stop” is marked with its corresponding f-number, and represents a halving of the light intensity from the previous stop. Modern electronically-controlled interchangeable lenses, such as those from Canon and Sigma for SLR cameras, have f-stops specified internally in 1/8-stop increments, so the cameras’ 1/3-stop settings are approximated by the nearest 1/8-stop setting in the lens. The F number can be displayed as 1:X instead of f/X(like in our example).
Lenses with larger apertures are faster because, for a given ISO speed, the shutter speed can be made faster for the same exposure. A smaller aperture means that objects can be in focus over a wider range of distance (depth of field).
Portrait and indoor (sports and theater also) photography often requires lenses with large maximum apertures in order to be capable of faster shutter speeds (and narrower depth of fields) in order to combat the low light problems with no camera shake.
The narrow depth of field in a portrait, as well as in macro photography, helps isolate the subject from the background.
Minimum apertures for lenses are almost as important as maximum apertures. This is primarily because the minimum apertures are rarely used due to photo blurring from lens diffraction, and because these may require long exposure times.
For cases where extreme depth of field is desired, then smaller minimum aperture (larger maximum f-number) lenses allow a wider depth of field.
It’s also good to know that lenses typically have fewer aberrations when they perform the exposure stopped down one or two f-stops from their maximum aperture.