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Focal length is a characteristic of the lens that, together with the size of the sensor that captures the image, determines how wide or narrow is the field of view recorded in the image.
If we use a fullframe sensor (36x24mm, the size of the old-times standard film), we have:
* 50mm is considered "normal" focal length. This lens will give us a field of view that looks similar to what our eyes can see in everyday life. That's why it is one focal length that is used very often.
* 35mm or less is considered "wide angle" focal length. The field of view is much wider, the camera "sees more to the sides". These focal lengths are often used for landscapes, buildings, and groups of people (specially if getting a couple of steps further away from them is not an option).
* 75mm or more is considered "telephoto" focal length (actually, "telephoto" is a related but different thing, but I prefer to skip the details, be less specific in my language, and stick to the important stuff). The field of view is very narrow, the lens can "see far". Often used for portraits and to take pictures of distant things.
A picture taken with a 28mm focal length:
And a picture taken from the same spot with a 90mm focal length:
All the previous explanation is valid in general, but the specific focal lengths I've detailed are only valid for cameras with fullframe sensors (36x24mm), which are usually expensive. If you are reading this, your camera probably has a smaller sensor. In that case, you need to find out what is your camera's crop factor (a good place to search for it is here), and then calculate equivalent focal lengths (which determine the field of view) by multiplying the focal length of the lens by the crop factor of the camera.
For example, my camera is a Canon with an APS-C sensor, which means its crop factor is 1.6x. To calculate the equivalent focal length (which will tell me if the lens will work as a wide angle or telephoto), I have to multiply the focal length of the lens by 1.6. So my "normal" lens is a 35mm, which gives me the same field of view that a 56mm lens whould deliver on a fullframe sensor. And when I use a 50mm on my camera, it is not "normal", but "telephoto", because it is equivalent to an 80mm lens on a camera with a fullframe sensor.
(in case anybody is interested, a telephoto is a lens which is shorter than its focal length; this is particularly useful for lenses with a long focal length, that's why people usually think a telephoto is a lens with a long focal length: a 500mm lens, if it is not a telephoto, is half a meter long; if it is telephoto, it will still be huge, but can be a bit shorter; a lot more info in this great blog)