In 35mm camera terms any lens 35mm and under can be considered wide angle. Common focal lengths are 35, 28, 24, 21, 20, 18 and 14 mm with some barrel distortion present in some cases although not as severe as the 6 to 8mm focal lengths of ultra-wide fisheye lenses. So why do wide angle lenses matter?
If you care to read some of the many informative articles online you can find some in depth and mathematical explanations on wide angle lenses. My math, although not the worst, is lost on the numbers involved though for calculating the angle of view of your chosen lens.
In layman’s terms a wide angle lens will have a wider field of view meaning you can fit more of the scene in front of you in. This might mean from a distance you can capture a sweeping panorama or when up close to an object you can still fill the frame with a wide view. This makes them ideal then for landscape and street photography.
In this (admittedly crude) example of a photo taken on a 24mm lens the red lines depict the full field of view captured by the camera. The orange lines meanwhile depict a much narrower field of view you might expect with a standard lens, for example 50mm. It’s clear that had a standard or telephoto lens been used it would not have been possible to capture the same scene and the photo would lose some of its impact.
It’s worth mentioning also that as wide becomes ultra-wide some perspective distortions can become apparent although depending on the subject the effect can be both creative and desirable.